a truck with a mass of 1150 kg and a velocity of 13 m/s collided into a parked car with a mass velocity does the car move forward after the collision

Yes

Explanation:

The truck has momentum since it is moving and momentum is a product of mass and velocity. After impact, part of momentum that the truck had is transferred to the car hence the car initially at rest moves a significant diatance. Here, we utilize the formula MV = (m+M) v where M and V represent mass and velocity of the truck while m is the mass of car, v is the common velocity. Note that some letters are capital while others small, don't confuse these.