1.) A car with an initial velocity of 3.5 m/s coasts with the engine off and the transmission in neutral. If the comined effect of air resistance and rolling friction causes a deceleration of 0.50 m/s², after how long a time will the car come to a complete stop?
2.) A car accelerates from rest at a constant rate of 2.0 m/s² for 5.0 s. What is the speed of the car at the end of that time? (b) How far does the car travel in this time?
3.) An experimental rocket car starting from rest reaches a speed of 560 km/h after a straight 400-m run on a road. Assuming that the acceleration is constant, (a) what was the time of the run, and (b) what is the magnitude of the acceleration?
Starting from rest, under a constant accelleration a for a time t the distance
run is:
s = (a t^2)/2
and a speed of:
v = a t
(with every thing in m, m/s, and m/s^2)
So in this case:
560*1000/3600 = a t,
and:
400 = (a t^2)/2 = (a t) t/2 = (560*1000/3600) t/2
so:
t = (400*2)/(5600*1000/3600) ~= 5.14 s,
and:
a = (560*1000/3600)/5.14 ~= 30.26 m/s^2
RonL