A train was moving at the rate of 54 km h^-1 when brakes were applied. It came to rest within a distance of 225 m. Calculate the retardation produced in the train.

Suppose two cars A and B are moving with uniform velocities with respect to ground along parallel tracks and in the same direction. Let the velocities of A and B be 35 km h^-1 due east and 40 km h^-1 due east respectively. What is the relative velocity of car B with respect to A?

Consider two trains A and B moving along parallel tracks with the same velocity in the same direction. Let the velocity of each train be 50 km h^-1 due east. Calculate the relative velocities of the trains.

A swimmer's speed in the direction of flow of a river is 12 km h^-1. Against the direction of flow of the river the swimmer's speed is 6 km h^-1. Calculate the swimmer's speed in still water and the velocity of the river flow.

The position vector for a particle is represented be \(\vec r=3t^2\hat i+5t\hat j+6\hat k\), find tht velocity and speed of the particle at t = 3 sec?