Question

A small car of mass 985 kg is parked behind a small truck of mass 1551 kg on a level road. The brakes of both the car and the truck are off so that they are free to roll with negligible
friction. A 83 kg woman sitting on the tailgate of the truck shoves the car away by exerting a constant force on the car with her feet. The car accelerates at 0.3 m/s2. What is the acceleration of the truck?
Answer in units of m/s2

Answer 1

The mass of the car, m = 985 kg, acceleration of the car, a = 0.3 m/s^2
According to Newton's 2nd law, force exerted on the car,
F = ma = 985 x 0.3 = 295.5 N
According to Newton's 3rd law, the same force in the opposite direction will be exerted on the truck.

Mass of the truck with the woman, M = 1551 + 83 = 1634 kg
Force acting on the truck, F = 1634 N [ same as the force on the car ]
F = M•a1 or, a1 = F/M = 295.5/1634 = 0.18 m/s^2
So the acceleration of the truck will be 0.18 m/s^2 and it's direction will be opposite of the car's acceleration.