The driver of a car is going 90 km/hr suddenly sees a barrier40m ahead. It takes the driver .75 sec to apply the brakes, and the average acceleration during braking is -10m/s^2. Will the car hit the barrier and use calculation to show work.

Answer 1

90,000 m / 3600 s = initial speed = Ui

distance = .75 Ui + (Ui/2) t
to find t:
u = Ui - 10 t
when u = 0 we are stopped
so
t = Ui/10
so in the end

distance = .75 Ui + (1/2) Ui^2/10

Answer 2

Vo = 90,000m/3600s = 25 m/s.

d1 = Vo*t = 25m/s * 0.75s. = 18.75 m.
d2 = 40 - 18.75 = 21.25 m. = Required stopping distance.
Vf^2 = Vo^2 + 2a*d.
Vf = 0.
Vo = 25 m/s.
a = -10 m/s^2.

If d is => 21.25 m, the car will hit the barrier.