Question

An unloaded bus can be stopped by applying brakes on straight road after covering a distance x. Suppose the passanger adds 50% of its weight as the load and the braking force remains the same how far will the bus go after the application of the brakes ? (Velocity of the bus in both case is same)

Answer 1

suppose mass of bus = m
after brakes are applied , braking force acts on bus which stops it .
braking force= F
decceleration of bus , a = - F/m
by kinematics third law , V^2 = U^2 + 2 a x ( as bus finally stops so V=0)
0 = U^2 + 2 (-a) x ==> x = U^2 / (2*a)
now passanger adds 50% of its weight as the load so new mass of bus = m' = m+ 50% of m = m+ (50/100)m= m'=1.5*m
so same braking force F
new deceleration a' = - F/m'= - F / (1.5 m) = a / 1.5
by kinematics third law , V^2 = U^2 + 2 a x ( as bus finally stops so V=0)
==> 0 = U^2 + 2* (-a') x' ==> x' = U^2 / (2* a') = U^2 / (2* a/1.5) = 1.5 *x
so now bus will travel 1.5*x distance.