The 2007 BMW Z4 Coupe 30si can accelerate from 0 to 57 mph i

The 2007 BMW Z4 Coupe 3.0si can accelerate from 0 to 57 mph in 4.6 s, and its maximum speed is X_max = 140 mph. Assuming the car accelerates from 0 to 57 mph at a constant rate and that it can continue to accelerate at this rate without redlining, find how far the car travels and how long it takes to reach its maximum speed.

Solution

from v= u+at

u=0, v=57mph=83.6fps , t=4.6s

a=v/t=83.6/4.6=18.17ft/s2

now for maximum speed

v=u+at

v=140mph=205.33fps, u=0, a=18.17f/s2

t=v/a=11.3s

s= ut+0.5at2=0+0.5*18.17*11.3*11.3=1160 ft