(7%) Problem 8: The position of an athlete was measured at various times and the

Question

(7%) Problem 8: The position of an athlete was measured at various times and the results are shown in the table and graphed in the figure Position vs Time 30.00 Time (s) 0.00 2.50 5.00 7.50 10.0 12.5 15.0 20.0 Position (m 0.00 8.75 17.5 10.0 2.50 2.50 5.00 25.0 25.00 20.00 15.00 10.00 5.00 0.00 0.00 2.50 .00 7.50 10.00 12.30 15.00 17.50 20.00 Time (s) 50% Part (a) Take the slope of the curve to find the athlete's instantaneous velocity, in meters per second, at time 2.5 s 50% Part (b) Take the slope of the curve to find the athlete's instantaneous velocity, in meters per second, at time -7.5 s Grade Summary Deductions 0%

Explanation / Answer

Given

position vs time graph

we know that the slope of the curve is the velocity

Part (a)

the slope at time t = 2.5 s is

here the slope v = x2-x1/t2-t1

v = (8.75-0)/(2.5-0) m/s

v = 3.5 m/s

Part (b)

at t= 7.5 s is

the slope v = ( x2-x1)/(t2-t1 )

v = (10-17.5)/(7.5-5) m/s

v = -3.0 m/s

-ve sign is because the curve is a negative slope curve

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