Derivative Problem

A Honda Civic travels in a straight line along a road. It’s distance x from a stop sign is given as a function of time t by the equation, where and. Calculate the velocity of the car for each of the time given: (a) t = 2.00s; (b) t = 4.00s; (c) What will be the time when the acceleration is equal to zero?
Solution:
By getting the derivative of the distance as a function of time we can get the velocity as a function of time.

  Substitute the values of α and β
 

a) Given t = 2.00s b) Given t = 4.00s
Use: Use:

c) First get the equation of the acceleration as a function of time by getting the derivative of the velocity as a function of time.   Since = 0,
 

Worksheet
Name: Jhaneza Urbano
Year & Section: Y4 - Temperance

Goal: My goal is to know how far a car can go with a given time using Derivatives.

Role: I am an automotive engineer.

Audience: My audience are my co-workers.

Situation: I and my co-worker engineers are to test a Honda Civic. We are to calculate the time of acceleration when it starts from rest.

Procedure: I. Let x be equal to distance, t equal to time and a equal to acceleration. II. Solve for the function of time using the derivative of distance. III. Calculate the velocity of the car for each given time. IV. By using the equation of acceleration as function of time. Get the derivative of velocity as function of time.
Introduction

The derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity. The derivative of a function at a chosen input value