Question

An 1100-kg car at rest at a stop sign is hit from the rear by a 2200-kg truck. The car and truck remain locked together and skid 4.6m before stopping. if the coefficient of friction between the vehicles and the road is 0.7. What was the truck's initial velocity ?

Answer 1

Given :

mass of car , m = 1100 kg

mass of wooden block , M = 3300 kg

distance traveled after collision = 4.6 m

coefficient of friction = 0.7

To find :

Truck's initial velocity .

Solution :

Let initial velocity of truck be v .

Let combined velocity of truck+car system is u .

by , conservation of linear momentum ,

  2200 * v = ( 1100 + 2200 ) * u

=> u = (2/3) v

acceleration of the car+truck system = μg

                                                             = 0.7 * 9.8

                                                             = 6.86 m/$s^{2}$ (retarding in nature)

by 3rd equation of motion , where final velocity is 0 (zero) ,

    0 = (2/3)v * (2/3)v - ( 2 * 6.86 * 4.6 )

=> v = 11.91 m/s

Truck's initial velocity is 11.91 m/s .