A sports car claims that it can start from rest and reach 60 mph (26.8 m/s) in a

Question

A sports car claims that it can start from rest and reach 60 mph (26.8 m/s) in a distance of 33.5 meters. To reach its maximumm speed, it accelerates at this constant rate for 11.25 seconds.

a) How many seconds does it take to reach 60 mph?
- I got 1.25 seconds
b) What is the maximum speed of this car?
- Using kinematics I got 120.6 m/s
c) If the mass is 1900 kg, what force must the car provide to keep it traveling at this maximum speed ( Hint: don't forget friction)

- I know that Fnet= mass x acceleration, and that gives me 1900 x 10.72 = 20,368 N
but this is not taking into account friction. What role does friction play and how can I calculate it properly?

d) I was driving this car at a maximum speed on a test track when a deer ran out in front of me. My reaction time was 0.5 seconds, before I hit the brakes. Assuming that the engine is no longer applying any forward force, and my wheels lock up, how far will I travel before I come to a stop after seeing the deer (give answer in miles, using: 1 Km = 0.62 miles)?

e) How much time will elapse from the time that I see the deer until I stop?

Explanation / Answer

The speed of the car v = 26.8m/s the distance traveled x = 33.5m (a) From kinematic equations v^2 = 2ax then acceleration a = v^2 /2x = (26.8)^2 / 2(33.5) = 10.72 m/s^2 the time taken to reach v = at t = v/a = 26.8/10.72 = 2.5s (b) The maximum speed vmax = at = (10.72)(11.25) = 120.6 m/s (c) If mass m = 1900kg the force provide to keep it traveling maximum speed F = ma = 1900*10.72 = 20368 N here the F is the net force means it includes all the forces acting on it (d) the speed of the car V = 120.6m/s the distance traveled in time t= 0.5s d1 = 120.6*0.5 = 60.3m and the distance traveled until stopping v^2 +2ad2 = 0 then d2 = v^2 /2a = (120.6)^2/2(10.72) = 678.4 m therefore the total distance d = 60.3 +678.4 = 738.7 m (e) the time taken to stop v -at = 0 t ' = v/a = 120.6/10.72 =11.25s therefore t = 0.5 +11.25 = 11.75 sec

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