Chapter 4, Problem 98A

(a)

To determine

The instantaneous speed of car B at $2.0\text{s}$ .

Answer to Problem 98A

The instantaneous speed of car B at $2.0\text{s}$ is $0\text{m/s}$ .

Explanation of Solution

Given info:

The position versus time graph for car $\text{A}$ and car $\text{B}$ .

Formula used:

The object’s speed at a given instant of time is known as the instantaneous speed of the object. The slope of the position-time graph of an object at an instant of time represents the instantaneous speed of the object at that instant of time.

The instantaneous speed of an object is the slope of the object’s position-time graph at that instant of time.

Calculation:

Refer to the position-time graph of the car $\text{A}$ and car $\text{B}$ .

The car $\text{B}$ is at rest at time equal to $2.0\text{s}$ and the car is not moving.

Hence, the instantaneous speed of the car $\text{B}$ at a time $t=2.0\text{s}$ is $0\text{m/s}$ .

Conclusion:

Thus, the instantaneous speed of the car $\text{B}$ at the time $t=2.0\text{s}$ is $0\text{m/s}$ , as the car is at rest.

(b)

To determine

The instantaneous speed of car B at $9.0\text{s}$ .

Answer to Problem 98A

The instantaneous speed of car B at $9.0\text{s}$ is $0\text{m/s}$ .

Explanation of Solution

Given info:

The position versus time graph for car $\text{A}$ and car $\text{B}$ .

Formula used:

The object’s speed at a given instant of time is known as the instantaneous speed of the object. The slope of the position-time graph of an object at an instant of time represents the instantaneous speed of the object at that instant of time.

The instantaneous speed of an object is the slope of the object’s position-time graph at that instant of time.

Calculation:

Refer to the position-time graph of the car $\text{A}$ and car $\text{B}$ .

The instantaneous speed of an object is the slope of the object’s position-time graph at that instant of time.

The slope of the position-time graph is almost horizontal and parallel to the horizontal axis at time $t=9.0\text{s}$ .

The slope of the position-time graph is almost zero at time $t=9.0\text{s}$ .

Hence, the instantaneous speed of the car $\text{B}$ at time $t=9.0\text{s}$ is almost equal to $0\text{m/s}$ .

Conclusion:

Thus, the instantaneous speed of the car $\text{B}$ at time $t=9.0\text{s}$ is $0\text{m/s}$ .

(c)

To determine

The instantaneous speed of car A at $2.0\text{s}$ .

Answer to Problem 98A

The instantaneous speed of car A at $2.0\text{s}$ is $1\text{m/s}$ .

Explanation of Solution

Given info:

The position versus time graph for car $\text{A}$ and car $\text{B}$ .

Formula used:

The object’s speed at a given instant of time is known as the instantaneous speed of the object. The slope of the position-time graph of an object at an instant of time represents the instantaneous speed of the object at that instant of time.

The instantaneous speed of an object is the slope of the object’s position-time graph at that instant of time.

Calculation:

Refer to the position-time graph of the car $\text{A}$ .

Find the slope of the position-time graph of the car $\text{A}$ at the time $t=2.0\text{s}$ .

  $\begin{array}{c}{\left(\text{Slope}\right)}_{\text{t}=2.0\text{s}}=\left(\frac{1\text{m}-0\text{m}}{2.0\text{s}-1.0\text{s}}\right)\\ =\left(\frac{1\text{m}}{1.0\text{s}}\right)\\ =1\text{m/s}\end{array}$

The slope of the position-time graph of the car $\text{A}$ at a time $t=2.0\text{s}$ is $1\text{m/s}$ .

The instantaneous speed of an object is the slope of the object’s position-time graph at that instant of time.

Conclusion:

Thus, the instantaneous speed of the car $\text{A}$ at time $t=2.0\text{s}$ is $1\text{m/s}$ .