A car can go from 0 to 100 km/h in 5.02 s. It takes another 8.97 s to reach the

Question

A car can go from 0 to 100 km/h in 5.02 s. It takes another 8.97 s to reach the speed 234 km/h. Assume constant acceleration. (Assume the car is traveling in the +x-direction.)

(a) Calculate the acceleration of the car over the first 5.02 s. (Indicate the direction with the sign of your answer.)

b)How much distance does the car have to cover to reach a speed of 234 km/h

(c) The speed of the car is limited to 374 km/h to protect the tires. When the car maintains the same acceleration that it had at 234 km/h, how long would it take the car to reach 374 km/h from rest? (Assume the car goes from 0 to 100 km/h with the acceleration in part (a).)

Explanation / Answer

given,

car can go from 0 to 100 km/h or 27.7778 m/s in 5.02 s

It takes another 8.97 s to reach the speed 234 km/h

acceleration = change in speed /time

acceleration from 0 - 100 km/h or 0 - 27.7778 m/s = 27.7778 / 5.02

acceleration from 0 - 100 km/h or 0 - 27.7778 m/s = 5.53 m/s^2

acceleration from 100 - 234 km/h or 27.7778 - 65 m/s = (65 - 27.7778) / 8.97

acceleration from 100 - 234 km/h or 27.7778 - 65 m/s = 4.1496 m/s^2

distance covered in 5.02 sec

s = ut + 0.5 * at^2

s = 0 + 0.5 * 5.53 * 5.02^2

s = 69.679 m

distance covered in another 8.97 sec

s1 = 27.7778 * 8.97 + 0.5 * 4.1496 * 8.97^2

s1 = 416.107 m

total distance covered = s + s1

total distance covered = 69.679 + 416.107

total distance covered = 485.786 m

374 km/h = 103.889 m/s

v = u + at

103.889 = 27.7778 + 4.1496 * t

t = 18.34 sec

time car will take to reach 374 km/h = 18.34 + 5.02

time car will take to reach 374 km/h = 23.36 sec

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