Answer: The graph in Fig. E2.31 shows the velocity of a

Chapter 2, Problem 31E

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QUESTION:

The graph in Fig. E2.31 shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at t = 3 s, at t = 7 s, and at t = 11 s. (b) How far does the officer go in the first 5 s? The first 9 s? The first 13 s?

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QUESTION:

The graph in Fig. E2.31 shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at t = 3 s, at t = 7 s, and at t = 11 s. (b) How far does the officer go in the first 5 s? The first 9 s? The first 13 s?

ANSWER:

Step 1 of 3

According to the kinematic equation, the acceleration is given by

\(a=\frac{\Delta v}{\Delta t} \quad \Rightarrow(1)\)

The change in velocity is given by

\(\Delta v=v_{f}-v_{i} \quad \Rightarrow(2)\)

AAnd The change in time is given by

\(\Delta t=t_{f}-t_{i} \quad \Rightarrow(3)\)

Where :

\(v_{i}\) is the initial velocity of the interval.

\(v_{f}\) is the final velocity of the interval.

\(t_{i}\) is the beginning of the interval.

\(t_{f}\) is the end of the interval.

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