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## Homework Statement

A test driver is testing a new model car with a speedometer calibrated to read m/s rather than mi/h. The following series of speedometer readings were obtained during a test run along a long, straight road:

Time (s): 0 2 4 6 8 10 12 14 16

Speed (m/s): 0 0 2 6 10 16 19 22 22

I.e.,

(0 s, 0 m/s)

(2, 0)

(4, 2)

(6, 6)

(8, 10)

(10, 16)

(12, 19)

(14, 22)

(16, 22)

(a) Compute the average acceleration during each 2-s interval. Is the acceleration constant? Is it constant during any part of the test run?

(b) Make a velocity

_{x}-time graph of the data above, using scales of 1 cm = 1 s horizontally and 1 cm = 2 m/s vertically. Draw a smooth curve through the plotted points. By measuring the slope of your curve, find the instantaneous acceleration at t = 9 s, 13 s, and 15 s.

## Homework Equations

Average Acceleration

a = (Δv

_{x})/Δt

Instantaneous Acceleration

a = dv

_{x}/dt

## The Attempt at a Solution

I know how to get the answers for (a) and these are 0m/s/s, 1 m/s/s, 2 m/s/s, 2 m/s/s, 3 m/s/s, 1.5 m/s/s, 1.5 m/s/s, and 0 m/s/s. Acceleration is constant at 2 m/s/s and 1.5 m/s/s.

For (b), I made a graph as specified and tried finding the slopes of the tangent lines at t = 9 s, 13 s, and 15 s. My answers have not matched the book's, which are

**2.5 m/s/s, 1.5 m/s/s, and 0 m/s/s**, respectively. It makes sense that the instantaneous acceleration at 15 s is 0 m/s/s as there is no rise in the tangent line at t = 15 s and so the slope equals 0.

Thanks in advance.