Question

A toy car with a mass of 120 g moves to the right with a speed of 0.64 m/s. A small child drops a 36.0-g piece of clay onto the car. The clay sticks to the car and the car continues to the right. What is the change in speed of the car? Consider the frictional force between the car and the ground to be negligible.

Answer 1

this is a problem for which you must use momentum.
P=mv (P is momentum, m is the mass, and v is the velocity)

the toy car has a momentum because it has mass and velocity
however, it is in units of grams and you must convert it to units of kilograms. so
120g/1000g=.12kg
the momentum is
Px=(0.12kg)(0.64m/s)=+0.0768
this is in the x direction and since it is to the right we will say it is in the positive x direction

now convert the 36g to kilogram and you get
.036 kg

use conservation of momentum which states that the initial momentum has got to be conserved in your final momentum. also notice i did not calculate the momentum for the piece of clay. this is because it is in the y direction and since the car keeps moving in the x direction it is not necessary.

initial momentum=final momentum.
your initial momentum is only in the x direction so you will get
P: mv+mv=mv
P: .0768=(0.12kg+0.036kg)V

P: 0.0768=0.156V (where v is the final velocity)
P:0 .0876/0.156=V

V=0.4923m/s this is your final speed. however the question asks for the change in speed

change in speed equals= final velocity-initial velocity
.5959m/s - .73m/s= -.134