A father and son pushed their car to bring it to the side of a road as it had stalled in the middle of the road. They experienced that they had to push with all their might initially to move the car. But the push required to keep the car rolling was smaller. Explain.

Laws of friction can explain the cause.

As we want to move anybody we start applying force; frictional force comes into play. The friction here is static friction. As we increase our force the static friction also increases and after a certain value the body starts to move, and kinetic friction starts. On increasing the force again, the kinetic friction increases and the body gain a constant motion. Once the body starts moving the friction decreases, and the body continues to move with a constant force without increasing the force.

So the initial force required was large for overcoming the static friction and bringing the body into motion where only kinetic friction happens.