Q. 89 - Calculus

Question

Suppose your position $s\left(t\right)$ as you drive north along a straight highway is as shown in the graph that follows at the left, with t measured in hours and s measured in miles.

(a) Sketch a graph of your velocity v(t), and use the graph to describe your velocity over the course of the two-hour drive.

(b) Sketch a graph of your acceleration a(t), and use the graph to describe your acceleration over the course of the two-hour drive.

Step-by-Step Solution

Answer

Ans: Part (a).

Part (b).

Step 1. Given information:

Given, t measured in hours and s measured in miles. 

Step 2. Sketching a graph of your velocity v(t):

Here the objective is to draw the velocity graph of the function using the given graph:

The graph has increased in the interval from 0 to 2 hours. Therefore it is an increasing function. Hence the graph of the velocity function will be ,

Step 3. Sketching a graph of your acceleration a(t):

Here the object is to draw the acceleration graph of the function using the given graph The velocity graph has increased in the interval from 0 to 2 hours Therefore it is an increasing function.

Hence the graph of the acceleration function will bc: