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A drag racer accelerates from rest at an average rate of 13.2 m/s2 for a distance of 100. m. The driver coasts for 0.500 seconds and then uses the brakes and parachute to decelerate until the end of the track. The total length of the track is 180. m. What minimum deceleration rate must the racer have in order to stop prior to the end of the track

Sagot :

LammettHash

Over the first 100. m, the driver accelerates from rest to a speed v such that

v² - 0² = 2 (13.2 m/s²) (100. m)

⇒   v ≈ 51.4 m/s

For the next 0.500 s, the driver maintains this speed and covers a distance of

(51.4 m/s) (0.500 s) ≈ 25.7 m

The remaining length of track is

180. m - 100. m - 25.7 m = 54.3 m

and the driver must have a minimum acceleration a such that

0² - (51.4 m/s)² = 2a (54.3 m)

⇒   a ≈ -24.3 m/s²

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