Physics

Problem

The velocity

v(t)

(in meters per second) of a remote-controlled car for

0\le t\le 10

seconds is described verbally as follows: •

v(t)

increases linearly from

0\text{ m/s}

t=0

6\text{ m/s}

t=4

. •

v(t)

remains constant at

6\text{ m/s}

for

4<t<7

. •

v(t)

decreases linearly from

6\text{ m/s}

t=7

0\text{ m/s}

t=10

. Assume the graph of

v(t)

consists of the straight-line segments implied by the description. (a) Compute the total displacement of the car on the interval

0\le t\le 10

seconds. (b) Determine the average velocity of the car over the same interval and include units. (c) Calculate the instantaneous velocity of the car at the midpoint of the interval,

t=5

seconds. (d) Compare the average velocity from part (b) with the instantaneous velocity from part (c). Provide a brief explanation for any equality or inequality you observe. (a) Compute

\displaystyle \int_{0}^{10} v(t)\,dt

. (b) Determine the average velocity on

[0,10]

. (c) Calculate

v(5)

. (d) Compare the results from parts (b) and (c) with justification.

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