id stringlengths 4 6 | topic stringclasses 3
values | problem stringlengths 124 139 | params unknown | answer float64 0.03 75.2k | solution stringlengths 36 70 |
|---|---|---|---|---|---|
kin-0 | kinematics | A particle moves with initial velocity 10.4 m/s and constant acceleration 2.4 m/s^2 for 10.4 s. What is its displacement? Answer in meters. | {
"v0": 10.4,
"a": 2.4,
"t": 10.4
} | 237.95 | x = v0*t + 0.5*a*t^2 = 10.4*10.4 + 0.5*2.4*10.4^2 = 237.95 m |
kin-1 | kinematics | A particle moves with initial velocity 22.3 m/s and constant acceleration 6.8 m/s^2 for 5.7 s. What is its displacement? Answer in meters. | {
"v0": 22.3,
"a": 6.8,
"t": 5.7
} | 237.58 | x = v0*t + 0.5*a*t^2 = 22.3*5.7 + 0.5*6.8*5.7^2 = 237.58 m |
kin-2 | kinematics | A particle moves with initial velocity 7.0 m/s and constant acceleration 3.6 m/s^2 for 4.3 s. What is its displacement? Answer in meters. | {
"v0": 7,
"a": 3.6,
"t": 4.3
} | 63.38 | x = v0*t + 0.5*a*t^2 = 7.0*4.3 + 0.5*3.6*4.3^2 = 63.38 m |
kin-3 | kinematics | A particle moves with initial velocity 11.2 m/s and constant acceleration 5.4 m/s^2 for 7.3 s. What is its displacement? Answer in meters. | {
"v0": 11.2,
"a": 5.4,
"t": 7.3
} | 225.64 | x = v0*t + 0.5*a*t^2 = 11.2*7.3 + 0.5*5.4*7.3^2 = 225.64 m |
kin-4 | kinematics | A particle moves with initial velocity 28.5 m/s and constant acceleration 3.8 m/s^2 for 7.9 s. What is its displacement? Answer in meters. | {
"v0": 28.5,
"a": 3.8,
"t": 7.9
} | 343.73 | x = v0*t + 0.5*a*t^2 = 28.5*7.9 + 0.5*3.8*7.9^2 = 343.73 m |
kin-5 | kinematics | A particle moves with initial velocity 22.4 m/s and constant acceleration 7.5 m/s^2 for 4.2 s. What is its displacement? Answer in meters. | {
"v0": 22.4,
"a": 7.5,
"t": 4.2
} | 160.23 | x = v0*t + 0.5*a*t^2 = 22.4*4.2 + 0.5*7.5*4.2^2 = 160.23 m |
kin-6 | kinematics | A particle moves with initial velocity 17.8 m/s and constant acceleration 5.0 m/s^2 for 4.1 s. What is its displacement? Answer in meters. | {
"v0": 17.8,
"a": 5,
"t": 4.1
} | 115 | x = v0*t + 0.5*a*t^2 = 17.8*4.1 + 0.5*5.0*4.1^2 = 115.0 m |
kin-7 | kinematics | A particle moves with initial velocity 28.6 m/s and constant acceleration 2.7 m/s^2 for 9.4 s. What is its displacement? Answer in meters. | {
"v0": 28.6,
"a": 2.7,
"t": 9.4
} | 388.13 | x = v0*t + 0.5*a*t^2 = 28.6*9.4 + 0.5*2.7*9.4^2 = 388.13 m |
kin-8 | kinematics | A particle moves with initial velocity 3.9 m/s and constant acceleration 9.0 m/s^2 for 11.3 s. What is its displacement? Answer in meters. | {
"v0": 3.9,
"a": 9,
"t": 11.3
} | 618.68 | x = v0*t + 0.5*a*t^2 = 3.9*11.3 + 0.5*9.0*11.3^2 = 618.68 m |
kin-9 | kinematics | A particle moves with initial velocity 3.4 m/s and constant acceleration 2.5 m/s^2 for 9.5 s. What is its displacement? Answer in meters. | {
"v0": 3.4,
"a": 2.5,
"t": 9.5
} | 145.11 | x = v0*t + 0.5*a*t^2 = 3.4*9.5 + 0.5*2.5*9.5^2 = 145.11 m |
kin-10 | kinematics | A particle moves with initial velocity 28.4 m/s and constant acceleration 6.2 m/s^2 for 6.8 s. What is its displacement? Answer in meters. | {
"v0": 28.4,
"a": 6.2,
"t": 6.8
} | 336.46 | x = v0*t + 0.5*a*t^2 = 28.4*6.8 + 0.5*6.2*6.8^2 = 336.46 m |
kin-11 | kinematics | A particle moves with initial velocity 27.2 m/s and constant acceleration 1.7 m/s^2 for 7.5 s. What is its displacement? Answer in meters. | {
"v0": 27.2,
"a": 1.7000000000000002,
"t": 7.5
} | 251.81 | x = v0*t + 0.5*a*t^2 = 27.2*7.5 + 0.5*1.7*7.5^2 = 251.81 m |
kin-12 | kinematics | A particle moves with initial velocity 15.1 m/s and constant acceleration 1.7 m/s^2 for 9.8 s. What is its displacement? Answer in meters. | {
"v0": 15.1,
"a": 1.7000000000000002,
"t": 9.8
} | 229.61 | x = v0*t + 0.5*a*t^2 = 15.1*9.8 + 0.5*1.7*9.8^2 = 229.61 m |
kin-13 | kinematics | A particle moves with initial velocity 24.5 m/s and constant acceleration 1.2 m/s^2 for 4.7 s. What is its displacement? Answer in meters. | {
"v0": 24.5,
"a": 1.2,
"t": 4.7
} | 128.4 | x = v0*t + 0.5*a*t^2 = 24.5*4.7 + 0.5*1.2*4.7^2 = 128.4 m |
kin-14 | kinematics | A particle moves with initial velocity 6.1 m/s and constant acceleration 2.7 m/s^2 for 10.1 s. What is its displacement? Answer in meters. | {
"v0": 6.1,
"a": 2.7,
"t": 10.1
} | 199.32 | x = v0*t + 0.5*a*t^2 = 6.1*10.1 + 0.5*2.7*10.1^2 = 199.32 m |
kin-15 | kinematics | A particle moves with initial velocity 10.5 m/s and constant acceleration 1.6 m/s^2 for 2.5 s. What is its displacement? Answer in meters. | {
"v0": 10.5,
"a": 1.6,
"t": 2.5
} | 31.25 | x = v0*t + 0.5*a*t^2 = 10.5*2.5 + 0.5*1.6*2.5^2 = 31.25 m |
kin-16 | kinematics | A particle moves with initial velocity 27.0 m/s and constant acceleration 5.7 m/s^2 for 10.3 s. What is its displacement? Answer in meters. | {
"v0": 27,
"a": 5.7,
"t": 10.3
} | 580.46 | x = v0*t + 0.5*a*t^2 = 27.0*10.3 + 0.5*5.7*10.3^2 = 580.46 m |
kin-17 | kinematics | A particle moves with initial velocity 10.8 m/s and constant acceleration 8.0 m/s^2 for 4.0 s. What is its displacement? Answer in meters. | {
"v0": 10.8,
"a": 8,
"t": 4
} | 107.2 | x = v0*t + 0.5*a*t^2 = 10.8*4.0 + 0.5*8.0*4.0^2 = 107.2 m |
kin-18 | kinematics | A particle moves with initial velocity 9.0 m/s and constant acceleration 6.1 m/s^2 for 5.8 s. What is its displacement? Answer in meters. | {
"v0": 9,
"a": 6.1,
"t": 5.8
} | 154.8 | x = v0*t + 0.5*a*t^2 = 9.0*5.8 + 0.5*6.1*5.8^2 = 154.8 m |
kin-19 | kinematics | A particle moves with initial velocity 6.8 m/s and constant acceleration 6.5 m/s^2 for 3.9 s. What is its displacement? Answer in meters. | {
"v0": 6.8,
"a": 6.5,
"t": 3.9
} | 75.95 | x = v0*t + 0.5*a*t^2 = 6.8*3.9 + 0.5*6.5*3.9^2 = 75.95 m |
kin-20 | kinematics | A particle moves with initial velocity 2.4 m/s and constant acceleration 3.2 m/s^2 for 10.0 s. What is its displacement? Answer in meters. | {
"v0": 2.4,
"a": 3.2,
"t": 10
} | 184 | x = v0*t + 0.5*a*t^2 = 2.4*10.0 + 0.5*3.2*10.0^2 = 184.0 m |
kin-21 | kinematics | A particle moves with initial velocity 11.0 m/s and constant acceleration 2.5 m/s^2 for 7.3 s. What is its displacement? Answer in meters. | {
"v0": 11,
"a": 2.5,
"t": 7.3
} | 146.91 | x = v0*t + 0.5*a*t^2 = 11.0*7.3 + 0.5*2.5*7.3^2 = 146.91 m |
kin-22 | kinematics | A particle moves with initial velocity 19.9 m/s and constant acceleration 1.5 m/s^2 for 2.1 s. What is its displacement? Answer in meters. | {
"v0": 19.9,
"a": 1.5,
"t": 2.1
} | 45.1 | x = v0*t + 0.5*a*t^2 = 19.9*2.1 + 0.5*1.5*2.1^2 = 45.1 m |
kin-23 | kinematics | A particle moves with initial velocity 20.9 m/s and constant acceleration 8.7 m/s^2 for 2.9 s. What is its displacement? Answer in meters. | {
"v0": 20.9,
"a": 8.7,
"t": 2.9
} | 97.19 | x = v0*t + 0.5*a*t^2 = 20.9*2.9 + 0.5*8.7*2.9^2 = 97.19 m |
kin-24 | kinematics | A particle moves with initial velocity 3.8 m/s and constant acceleration 7.6 m/s^2 for 2.2 s. What is its displacement? Answer in meters. | {
"v0": 3.8,
"a": 7.6,
"t": 2.2
} | 26.75 | x = v0*t + 0.5*a*t^2 = 3.8*2.2 + 0.5*7.6*2.2^2 = 26.75 m |
kin-25 | kinematics | A particle moves with initial velocity 28.8 m/s and constant acceleration 5.2 m/s^2 for 3.6 s. What is its displacement? Answer in meters. | {
"v0": 28.8,
"a": 5.2,
"t": 3.6
} | 137.38 | x = v0*t + 0.5*a*t^2 = 28.8*3.6 + 0.5*5.2*3.6^2 = 137.38 m |
kin-26 | kinematics | A particle moves with initial velocity 17.9 m/s and constant acceleration 4.2 m/s^2 for 2.3 s. What is its displacement? Answer in meters. | {
"v0": 17.9,
"a": 4.2,
"t": 2.3
} | 52.28 | x = v0*t + 0.5*a*t^2 = 17.9*2.3 + 0.5*4.2*2.3^2 = 52.28 m |
kin-27 | kinematics | A particle moves with initial velocity 26.6 m/s and constant acceleration 5.5 m/s^2 for 4.3 s. What is its displacement? Answer in meters. | {
"v0": 26.6,
"a": 5.5,
"t": 4.3
} | 165.23 | x = v0*t + 0.5*a*t^2 = 26.6*4.3 + 0.5*5.5*4.3^2 = 165.23 m |
kin-28 | kinematics | A particle moves with initial velocity 8.4 m/s and constant acceleration 6.7 m/s^2 for 10.2 s. What is its displacement? Answer in meters. | {
"v0": 8.4,
"a": 6.7,
"t": 10.2
} | 434.21 | x = v0*t + 0.5*a*t^2 = 8.4*10.2 + 0.5*6.7*10.2^2 = 434.21 m |
kin-29 | kinematics | A particle moves with initial velocity 14.5 m/s and constant acceleration 1.3 m/s^2 for 7.6 s. What is its displacement? Answer in meters. | {
"v0": 14.5,
"a": 1.3,
"t": 7.6
} | 147.74 | x = v0*t + 0.5*a*t^2 = 14.5*7.6 + 0.5*1.3*7.6^2 = 147.74 m |
kin-30 | kinematics | A particle moves with initial velocity 24.1 m/s and constant acceleration 7.0 m/s^2 for 4.2 s. What is its displacement? Answer in meters. | {
"v0": 24.1,
"a": 7,
"t": 4.2
} | 162.96 | x = v0*t + 0.5*a*t^2 = 24.1*4.2 + 0.5*7.0*4.2^2 = 162.96 m |
kin-31 | kinematics | A particle moves with initial velocity 8.8 m/s and constant acceleration 3.6 m/s^2 for 2.8 s. What is its displacement? Answer in meters. | {
"v0": 8.8,
"a": 3.6,
"t": 2.8
} | 38.75 | x = v0*t + 0.5*a*t^2 = 8.8*2.8 + 0.5*3.6*2.8^2 = 38.75 m |
kin-32 | kinematics | A particle moves with initial velocity 18.7 m/s and constant acceleration 6.5 m/s^2 for 6.2 s. What is its displacement? Answer in meters. | {
"v0": 18.7,
"a": 6.5,
"t": 6.2
} | 240.87 | x = v0*t + 0.5*a*t^2 = 18.7*6.2 + 0.5*6.5*6.2^2 = 240.87 m |
kin-33 | kinematics | A particle moves with initial velocity 18.3 m/s and constant acceleration 7.5 m/s^2 for 9.8 s. What is its displacement? Answer in meters. | {
"v0": 18.3,
"a": 7.5,
"t": 9.8
} | 539.49 | x = v0*t + 0.5*a*t^2 = 18.3*9.8 + 0.5*7.5*9.8^2 = 539.49 m |
kin-34 | kinematics | A particle moves with initial velocity 28.8 m/s and constant acceleration 6.5 m/s^2 for 11.2 s. What is its displacement? Answer in meters. | {
"v0": 28.8,
"a": 6.5,
"t": 11.2
} | 730.24 | x = v0*t + 0.5*a*t^2 = 28.8*11.2 + 0.5*6.5*11.2^2 = 730.24 m |
kin-35 | kinematics | A particle moves with initial velocity 22.7 m/s and constant acceleration 5.9 m/s^2 for 7.3 s. What is its displacement? Answer in meters. | {
"v0": 22.7,
"a": 5.9,
"t": 7.3
} | 322.92 | x = v0*t + 0.5*a*t^2 = 22.7*7.3 + 0.5*5.9*7.3^2 = 322.92 m |
kin-36 | kinematics | A particle moves with initial velocity 18.0 m/s and constant acceleration 2.9 m/s^2 for 6.3 s. What is its displacement? Answer in meters. | {
"v0": 18,
"a": 2.9,
"t": 6.3
} | 170.95 | x = v0*t + 0.5*a*t^2 = 18.0*6.3 + 0.5*2.9*6.3^2 = 170.95 m |
kin-37 | kinematics | A particle moves with initial velocity 26.7 m/s and constant acceleration 2.5 m/s^2 for 7.0 s. What is its displacement? Answer in meters. | {
"v0": 26.7,
"a": 2.5,
"t": 7
} | 248.15 | x = v0*t + 0.5*a*t^2 = 26.7*7.0 + 0.5*2.5*7.0^2 = 248.15 m |
kin-38 | kinematics | A particle moves with initial velocity 8.5 m/s and constant acceleration 5.3 m/s^2 for 2.8 s. What is its displacement? Answer in meters. | {
"v0": 8.5,
"a": 5.3,
"t": 2.8
} | 44.58 | x = v0*t + 0.5*a*t^2 = 8.5*2.8 + 0.5*5.3*2.8^2 = 44.58 m |
kin-39 | kinematics | A particle moves with initial velocity 10.9 m/s and constant acceleration 6.5 m/s^2 for 7.9 s. What is its displacement? Answer in meters. | {
"v0": 10.9,
"a": 6.5,
"t": 7.9
} | 288.94 | x = v0*t + 0.5*a*t^2 = 10.9*7.9 + 0.5*6.5*7.9^2 = 288.94 m |
en-0 | energy | A 75.5 kg object is raised 79.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 75.5,
"h": 79.2,
"g": 9.81
} | 58,659.88 | PE = m*g*h = 75.5*9.81*79.2 = 58659.88 J |
en-1 | energy | A 62.4 kg object is raised 31.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 62.4,
"h": 31.8,
"g": 9.81
} | 19,466.18 | PE = m*g*h = 62.4*9.81*31.8 = 19466.18 J |
en-2 | energy | A 42.2 kg object is raised 29.5 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 42.2,
"h": 29.5,
"g": 9.81
} | 12,212.47 | PE = m*g*h = 42.2*9.81*29.5 = 12212.47 J |
en-3 | energy | A 65.1 kg object is raised 86.1 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 65.1,
"h": 86.1,
"g": 9.81
} | 54,986.13 | PE = m*g*h = 65.1*9.81*86.1 = 54986.13 J |
en-4 | energy | A 18.2 kg object is raised 5.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 18.2,
"h": 5.7,
"g": 9.81
} | 1,017.69 | PE = m*g*h = 18.2*9.81*5.7 = 1017.69 J |
en-5 | energy | A 25.3 kg object is raised 91.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 25.3,
"h": 91.8,
"g": 9.81
} | 22,784.12 | PE = m*g*h = 25.3*9.81*91.8 = 22784.12 J |
en-6 | energy | A 55.5 kg object is raised 16.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 55.5,
"h": 16.9,
"g": 9.81
} | 9,201.29 | PE = m*g*h = 55.5*9.81*16.9 = 9201.29 J |
en-7 | energy | A 53.6 kg object is raised 42.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 53.6,
"h": 42.8,
"g": 9.81
} | 22,504.92 | PE = m*g*h = 53.6*9.81*42.8 = 22504.92 J |
en-8 | energy | A 19.5 kg object is raised 47.6 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 19.5,
"h": 47.6,
"g": 9.81
} | 9,105.64 | PE = m*g*h = 19.5*9.81*47.6 = 9105.64 J |
en-9 | energy | A 41.1 kg object is raised 59.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 41.1,
"h": 59.2,
"g": 9.81
} | 23,868.91 | PE = m*g*h = 41.1*9.81*59.2 = 23868.91 J |
en-10 | energy | A 59.6 kg object is raised 48.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 59.6,
"h": 48.3,
"g": 9.81
} | 28,239.85 | PE = m*g*h = 59.6*9.81*48.3 = 28239.85 J |
en-11 | energy | A 40.4 kg object is raised 105.6 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 40.4,
"h": 105.6,
"g": 9.81
} | 41,851.81 | PE = m*g*h = 40.4*9.81*105.6 = 41851.81 J |
en-12 | energy | A 36.9 kg object is raised 10.4 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 36.9,
"h": 10.4,
"g": 9.81
} | 3,764.69 | PE = m*g*h = 36.9*9.81*10.4 = 3764.69 J |
en-13 | energy | A 0.6 kg object is raised 93.0 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 0.6000000000000001,
"h": 93,
"g": 9.81
} | 547.4 | PE = m*g*h = 0.6*9.81*93.0 = 547.4 J |
en-14 | energy | A 59.8 kg object is raised 93.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 59.8,
"h": 93.7,
"g": 9.81
} | 54,967.98 | PE = m*g*h = 59.8*9.81*93.7 = 54967.98 J |
en-15 | energy | A 61.0 kg object is raised 45.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 61,
"h": 45.7,
"g": 9.81
} | 27,347.34 | PE = m*g*h = 61.0*9.81*45.7 = 27347.34 J |
en-16 | energy | A 58.7 kg object is raised 102.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 58.7,
"h": 102.3,
"g": 9.81
} | 58,909.15 | PE = m*g*h = 58.7*9.81*102.3 = 58909.15 J |
en-17 | energy | A 59.5 kg object is raised 97.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 59.5,
"h": 97.2,
"g": 9.81
} | 56,735.15 | PE = m*g*h = 59.5*9.81*97.2 = 56735.15 J |
en-18 | energy | A 64.7 kg object is raised 18.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 64.7,
"h": 18.3,
"g": 9.81
} | 11,615.14 | PE = m*g*h = 64.7*9.81*18.3 = 11615.14 J |
en-19 | energy | A 49.2 kg object is raised 53.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 49.2,
"h": 53.7,
"g": 9.81
} | 25,918.41 | PE = m*g*h = 49.2*9.81*53.7 = 25918.41 J |
en-20 | energy | A 16.1 kg object is raised 51.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 16.1,
"h": 51.2,
"g": 9.81
} | 8,086.58 | PE = m*g*h = 16.1*9.81*51.2 = 8086.58 J |
en-21 | energy | A 43.4 kg object is raised 14.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 43.4,
"h": 14.9,
"g": 9.81
} | 6,343.73 | PE = m*g*h = 43.4*9.81*14.9 = 6343.73 J |
en-22 | energy | A 10.8 kg object is raised 103.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 10.8,
"h": 103.2,
"g": 9.81
} | 10,933.83 | PE = m*g*h = 10.8*9.81*103.2 = 10933.83 J |
en-23 | energy | A 35.2 kg object is raised 81.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 35.2,
"h": 81.2,
"g": 9.81
} | 28,039.33 | PE = m*g*h = 35.2*9.81*81.2 = 28039.33 J |
en-24 | energy | A 60.5 kg object is raised 20.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 60.5,
"h": 20.8,
"g": 9.81
} | 12,344.9 | PE = m*g*h = 60.5*9.81*20.8 = 12344.9 J |
en-25 | energy | A 75.0 kg object is raised 30.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 75,
"h": 30.3,
"g": 9.81
} | 22,293.23 | PE = m*g*h = 75.0*9.81*30.3 = 22293.23 J |
en-26 | energy | A 48.6 kg object is raised 24.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 48.6,
"h": 24.8,
"g": 9.81
} | 11,823.8 | PE = m*g*h = 48.6*9.81*24.8 = 11823.8 J |
en-27 | energy | A 76.5 kg object is raised 48.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 76.5,
"h": 48.3,
"g": 9.81
} | 36,247.46 | PE = m*g*h = 76.5*9.81*48.3 = 36247.46 J |
en-28 | energy | A 67.1 kg object is raised 114.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 67.1,
"h": 114.3,
"g": 9.81
} | 75,238.09 | PE = m*g*h = 67.1*9.81*114.3 = 75238.09 J |
en-29 | energy | A 10.1 kg object is raised 108.0 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 10.1,
"h": 108,
"g": 9.81
} | 10,700.75 | PE = m*g*h = 10.1*9.81*108.0 = 10700.75 J |
en-30 | energy | A 60.0 kg object is raised 100.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 60,
"h": 100.3,
"g": 9.81
} | 59,036.58 | PE = m*g*h = 60.0*9.81*100.3 = 59036.58 J |
en-31 | energy | A 9.7 kg object is raised 59.4 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 9.7,
"h": 59.4,
"g": 9.81
} | 5,652.33 | PE = m*g*h = 9.7*9.81*59.4 = 5652.33 J |
en-32 | energy | A 65.4 kg object is raised 87.5 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 65.4,
"h": 87.5,
"g": 9.81
} | 56,137.73 | PE = m*g*h = 65.4*9.81*87.5 = 56137.73 J |
en-33 | energy | A 22.9 kg object is raised 101.6 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 22.9,
"h": 101.6,
"g": 9.81
} | 22,824.34 | PE = m*g*h = 22.9*9.81*101.6 = 22824.34 J |
en-34 | energy | A 16.2 kg object is raised 20.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 16.2,
"h": 20.9,
"g": 9.81
} | 3,321.47 | PE = m*g*h = 16.2*9.81*20.9 = 3321.47 J |
en-35 | energy | A 68.5 kg object is raised 64.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 68.5,
"h": 64.2,
"g": 9.81
} | 43,141.44 | PE = m*g*h = 68.5*9.81*64.2 = 43141.44 J |
en-36 | energy | A 7.6 kg object is raised 56.4 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 7.6,
"h": 56.4,
"g": 9.81
} | 4,204.96 | PE = m*g*h = 7.6*9.81*56.4 = 4204.96 J |
en-37 | energy | A 58.2 kg object is raised 119.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 58.2,
"h": 119.2,
"g": 9.81
} | 68,056.29 | PE = m*g*h = 58.2*9.81*119.2 = 68056.29 J |
en-38 | energy | A 2.9 kg object is raised 89.1 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 2.9,
"h": 89.1,
"g": 9.81
} | 2,534.81 | PE = m*g*h = 2.9*9.81*89.1 = 2534.81 J |
en-39 | energy | A 43.1 kg object is raised 115.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules. | {
"m": 43.1,
"h": 115.9,
"g": 9.81
} | 49,003.79 | PE = m*g*h = 43.1*9.81*115.9 = 49003.79 J |
cir-0 | circuits | A 9.7 V source drives two resistors in parallel: 299 ohm and 469 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 9.7,
"r1": 299,
"r2": 469
} | 0.0531 | Rp = 299*469/(299+469) = 182.59 ohm; I = V/Rp = 9.7/182.59 = 0.0531 A |
cir-1 | circuits | A 7.0 V source drives two resistors in parallel: 380 ohm and 324 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 7,
"r1": 380,
"r2": 324
} | 0.04 | Rp = 380*324/(380+324) = 174.89 ohm; I = V/Rp = 7.0/174.89 = 0.04 A |
cir-2 | circuits | A 16.4 V source drives two resistors in parallel: 356 ohm and 290 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 16.4,
"r1": 356,
"r2": 290
} | 0.1026 | Rp = 356*290/(356+290) = 159.81 ohm; I = V/Rp = 16.4/159.81 = 0.1026 A |
cir-3 | circuits | A 16.2 V source drives two resistors in parallel: 219 ohm and 99 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 16.2,
"r1": 219,
"r2": 99
} | 0.2376 | Rp = 219*99/(219+99) = 68.18 ohm; I = V/Rp = 16.2/68.18 = 0.2376 A |
cir-4 | circuits | A 14.2 V source drives two resistors in parallel: 386 ohm and 286 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 14.2,
"r1": 386,
"r2": 286
} | 0.0864 | Rp = 386*286/(386+286) = 164.28 ohm; I = V/Rp = 14.2/164.28 = 0.0864 A |
cir-5 | circuits | A 6.6 V source drives two resistors in parallel: 179 ohm and 95 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 6.6,
"r1": 179,
"r2": 95
} | 0.1063 | Rp = 179*95/(179+95) = 62.06 ohm; I = V/Rp = 6.6/62.06 = 0.1063 A |
cir-6 | circuits | A 22.1 V source drives two resistors in parallel: 38 ohm and 498 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 22.1,
"r1": 38,
"r2": 498
} | 0.6259 | Rp = 38*498/(38+498) = 35.31 ohm; I = V/Rp = 22.1/35.31 = 0.6259 A |
cir-7 | circuits | A 14.7 V source drives two resistors in parallel: 266 ohm and 193 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 14.7,
"r1": 266,
"r2": 193
} | 0.1314 | Rp = 266*193/(266+193) = 111.85 ohm; I = V/Rp = 14.7/111.85 = 0.1314 A |
cir-8 | circuits | A 14.7 V source drives two resistors in parallel: 63 ohm and 404 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 14.7,
"r1": 63,
"r2": 404
} | 0.2697 | Rp = 63*404/(63+404) = 54.5 ohm; I = V/Rp = 14.7/54.5 = 0.2697 A |
cir-9 | circuits | A 8.2 V source drives two resistors in parallel: 463 ohm and 148 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 8.2,
"r1": 463,
"r2": 148
} | 0.0731 | Rp = 463*148/(463+148) = 112.15 ohm; I = V/Rp = 8.2/112.15 = 0.0731 A |
cir-10 | circuits | A 10.4 V source drives two resistors in parallel: 251 ohm and 15 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 10.4,
"r1": 251,
"r2": 15
} | 0.735 | Rp = 251*15/(251+15) = 14.15 ohm; I = V/Rp = 10.4/14.15 = 0.735 A |
cir-11 | circuits | A 5.8 V source drives two resistors in parallel: 335 ohm and 456 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 5.8,
"r1": 335,
"r2": 456
} | 0.03 | Rp = 335*456/(335+456) = 193.12 ohm; I = V/Rp = 5.8/193.12 = 0.03 A |
cir-12 | circuits | A 11.2 V source drives two resistors in parallel: 289 ohm and 278 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 11.2,
"r1": 289,
"r2": 278
} | 0.079 | Rp = 289*278/(289+278) = 141.7 ohm; I = V/Rp = 11.2/141.7 = 0.079 A |
cir-13 | circuits | A 19.8 V source drives two resistors in parallel: 470 ohm and 156 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 19.8,
"r1": 470,
"r2": 156
} | 0.1691 | Rp = 470*156/(470+156) = 117.12 ohm; I = V/Rp = 19.8/117.12 = 0.1691 A |
cir-14 | circuits | A 6.6 V source drives two resistors in parallel: 454 ohm and 176 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 6.6,
"r1": 454,
"r2": 176
} | 0.052 | Rp = 454*176/(454+176) = 126.83 ohm; I = V/Rp = 6.6/126.83 = 0.052 A |
cir-15 | circuits | A 12.4 V source drives two resistors in parallel: 142 ohm and 377 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 12.4,
"r1": 142,
"r2": 377
} | 0.1202 | Rp = 142*377/(142+377) = 103.15 ohm; I = V/Rp = 12.4/103.15 = 0.1202 A |
cir-16 | circuits | A 17.6 V source drives two resistors in parallel: 199 ohm and 406 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 17.6,
"r1": 199,
"r2": 406
} | 0.1318 | Rp = 199*406/(199+406) = 133.54 ohm; I = V/Rp = 17.6/133.54 = 0.1318 A |
cir-17 | circuits | A 22.2 V source drives two resistors in parallel: 249 ohm and 434 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 22.2,
"r1": 249,
"r2": 434
} | 0.1403 | Rp = 249*434/(249+434) = 158.22 ohm; I = V/Rp = 22.2/158.22 = 0.1403 A |
cir-18 | circuits | A 3.3 V source drives two resistors in parallel: 412 ohm and 11 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 3.3,
"r1": 412,
"r2": 11
} | 0.3081 | Rp = 412*11/(412+11) = 10.71 ohm; I = V/Rp = 3.3/10.71 = 0.3081 A |
cir-19 | circuits | A 14.9 V source drives two resistors in parallel: 54 ohm and 250 ohm. What total current flows? Answer in amperes, 4 decimals. | {
"v": 14.9,
"r1": 54,
"r2": 250
} | 0.3355 | Rp = 54*250/(54+250) = 44.41 ohm; I = V/Rp = 14.9/44.41 = 0.3355 A |
End of preview. Expand in Data Studio
physics-bench-micro
120 synthetic physics problems (kinematics, energy, circuits) with programmatically verified answers - the estate's first physics benchmark, rights-clean by construction.
Why synthetic
Every problem is generated and every answer is computed, not copied - zero rights questions, zero contamination from published benchmarks, infinitely regenerable with a new seed. Synthetic first, then rights-cleared external microbenches (Matbench, WeatherBench 2) on top, per the leader audit.
The verification contract
Each row carries explicit params; verify.py recomputes every answer from them -
a model answer passes only within tolerance. No regex extraction, no ambiguity.
Honest labels
- License: Apache-2.0 (generated by SZL Holdings, no third-party content)
- Seed: 20261110 - a new seed produces a fresh, equally valid battery
- Contamination-proof: regenerable on demand, so leakage is detectable
Generated by the estate's benchmark lane; answers machine-verified before publish.
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