A motor car running at the rate of 7 m s^-1` can be stopped by its brakes in 10m.Prove that total resistance to the motion when braeks are on is one-fourth of the weight of the car.

A trolley of mass 200 kg moves with a uniform speed of 36 km//h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^-1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley ? How much has the trolley moved from the time the child begins to run ?

A car travelling at a speed of 10m/s stops in 4s after the application of brakes. If we assume the retardation to be constant. Find the retardation.

A driver of a car travelling at 52kmh^(-1) applies the brake and accelerates uniformly in opposite direction. The car stop in 5 s. Another driver going at 3 km h^(-1) applied his brakes slowly and stop in 10 s. On the same graph paper plot the speed versus time graph for the two cars. Which of the two cars travelled farther after the brakes were applied ?

A boy throws a ball in air at 60^@ to the horizontal along a road with a speed of 10 m/s (36km/h). Another boy sitting in a passing by car observer the ball. Sketch the motion of the ball as observed by the boy in the car,if car has a speed of (18km/h). Give explanation to support your diagram.

Figure shows a conducting rod PQ in contact with metal rails RP and SQ, which are 0.25 m apart in a uniform magnetic field of flux density 0.4T acting perpendicular to the plane of the paper. Ends R and S are connected through a 5 Omega resistance. What is the emf when the rod moves to the right with a velocity of 5ms^(-1) ? What is the magnitude and direction of the current through the 5 Omega resistance? If the rod PQ moves to the left with the same speed, what will be the new current and its direction?

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s^-1. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it ? Mass of mars = 6.4xx10^23 kg , radius of mars = 3395 km, G = 6.67xx10^-11 N m^2 kg^-2 .

A car of 1000 kg moving with a velocity of 30 m//s stops with uniform acceleration after covering a distance of 50 m on application of brakes. Find the force applied by the brakes on the car and also work done.

Height of a tank in the form of an inverted cone is 10 m and radius of its circular base is 2 m. The tank contains water and it is leaking through a hole at its vertex at the rate of 0.02m^(3)//s. Find the rate at which the water level changes and the rate at which the radius of water surface changes when height of water level is 5 m.