Chapter 13.3, Problem 36E

a.

To determine

To estimate : What was the initial velocity of the car.

Answer to Problem 36E

The initial velocity is zero.

Explanation of Solution

Given information:

The graph shows the position function of a car. Use the shape of the graph to explain.

Calculation :

The velocity of a car at point $a$ is the slope of the tangent to the graph at $x=a$.

Since, the body started from rest. Therefore, the initial velocity is zero.

Hence,

The initial velocity is zero.

b.

To determine

To estimate : The car was going faster at B or at C.

Answer to Problem 36E

The car was going faster at point C.

Explanation of Solution

Given information:

The graph shows the position function of a car. Use the shape of the graph to explain.

Calculation :

The velocity of a car at point $a$ is the slope of the tangent to the graph at $x=a$.

Since, the slope of the tangent at point C is greater than the slope of tangent at B. Therefore, the card was going faster at C

Hence,

The car was going faster at point C.

c.

To determine

To estimate : The car was slowing down or speeding up at point A, B and C.

Answer to Problem 36E

The car was speeding up at A, slowing down at B and again speeding up at C.

Explanation of Solution

Given information:

The graph shows the position function of a car. Use the shape of the graph to explain.

Calculation :

The velocity of a car at point $a$ is the slope of the tangent to the graph at $x=a$.

Since, the slope of the tangent at point A is greater, therefore the car was speeding up at point A.

The slope at point B is smaller, therefore the car was slowing down at point B and again the slope at point C is greater, therefore the car again speed up at point C.

Hence,

The car was speeding up at A, slowing down at B and again speeding up at C.

d.

To determine

To estimate : What happened between point D and E.

Answer to Problem 36E

The velocity of the car was constant between D and E.

Explanation of Solution

Given information:

The graph shows the position function of a car. Use the shape of the graph to explain.

Calculation :

The velocity of a car at point $a$ is the slope of the tangent to the graph at $x=a$.

Since, the slope between D and E is zero. Therefore, the velocity of the car was constant between D and E.

Hence,

The velocity of the car was constant between D and E.