Model: bartowski/Hercules-2.0-Mistral-7B-exl2
Author: bartowski
Pipeline: text-generation
Library: transformers
Tags: transformers, not-for-all-audiences, chemistry, math, code, physics, text-generation, dataset:Locutusque/hercules-v2.0, license:apache-2.0, endpoints_compatible, region:us
Card metadata: license: apache-2.0
library_name: transformers
tags: not-for-all-audiences, chemistry, math, code, physics
datasets: Locutusque/hercules-v2.0
widget: example_title: Derivative
text: 
user
In this task, you are given a description of an object and its surroundings. Your task is to describe the motion of the object mentioned in the description using differential equations. The answer should be a mathematical expression in t. Description: A ball is thrown up at 30 ft/sec from 3 feet off the ground. Solve this step-by-step, explaining each step in detail.


assistant

output: text: Let h(t) be the height of the ball at time t after it was thrown. We know that when the ball is thrown, it has an initial velocity v0 = 30 ft/sec and initial height y0 = 3 ft. We also know that the acceleration due to gravity g = -32 ft/sec^2.

To solve for the motion of the ball, we can use the equation for vertical motion with acceleration due to gravity:

h(t) = v0 * t + (1/2) * g * t^2 + y0

Substituting the values given in the problem, we get:

y(t) = (30)(t) + (1/2)(-32)(t)^2 + 3

Now, let's simplify the equation:

y(t) = 30t - 16t^2 + 3

This is the final solution for the height of the ball as a function of time.
quantized_by: bartowski
pipeline_tag: text-generation
Likes: 0 | All-time downloads: 3
Created: 2024-02-10 14:00:39