Question

A driver in an older car slams on his brakes and the wheels lock. It slides to rest under the influence of friction in 1.25 s. If the coefficient of kinetic friction is 0.450, what was the car's initial speed?

Answer 1

Using 1st kinematic equation

V = U + a*t

Given that finally car slides to rest, So V = final speed = 0 m/s

U = Initial speed = ?

t = time taken by car to come into rest = 1.25 sec

Using force balance on car in horizontal direction:

F_net = Ff

Ff = friction force = -$\mu_k$*N = -$\mu_k$*m*g

From newton's 2nd law: F_net = m*a

So,

m*a = -$\mu_k$*m*g

a = acceleration due to friction force = -$\mu_k$*g = -0.450*9.81

So,

U = V - a*t

U = 0 - (-0.450*9.81)*1.25

U = 5.52 m/sec = Car's Initial speed

Let me know if you've any query.