A can travels a certain distance along a straight road (in the +x direction). Th

Question

A can travels a certain distance along a straight road (in the +x direction). The distance the car travels as a function of time is shown the figure below. When the car changes speed it does so uniformly. Select the appropriate choice for each statement. Less than The speed at 4 sec is ..... the speed at 73 sec. Equal to The speed is ..... zero at 29 sec. True The x-acceleration is ..... zero at 36 sec. Greater than The acceleration magnitude at 15 sec is ..... the acceleration magnitude at 36 sec. Equal to The x-acceleration is ..... zero at 7 sec. Greater than At 4 sec, the speed is an high as it gets. By extrapolating the straight sections of the graph, you can estimate the time during which the speed is changing. This, with the change in speed, should let you estimate the magnitude of the acceleration.

Explanation / Answer

From the plot

a. Soeed at 0 is the slope of the graph

slope =300/15 = 20 m/s

so speed at t = 0 is 20 m/s

b. the highest slope is between the 35 to 60 s mark, hence this is the region of highest speed. SO the statement that the speed is highest at 4s is False

c. at 15 second, the speed reduces from 20 m/s to 0 m/s, where as the speed jumps from 0 to a higher value at 37 s, hence the acceleration magnitude at 37 s is higher, so this statement is true

d. at 4 s, the velocity is constant ( constant slope of the curve) hence the acceleration is 0

so this statement is true

e. at 70 s, the slope is lower than the slope at t = 4 s

SO SPEED AT T = 70 S IS LESS THAn the speed at 4 s

f. at 37 s, the speed of the object changesd, meaning there is acceleration, hence this statement is false

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