Motion in a Pla...

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T min. A man cycling with a speed of 20 km/h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min. in the opposite direction. The period T of bus service is

A car leaves station X for station Y every 10 minutes. The distance between X and Y is 60 km. The car travels at a speed of 60 km/h. A man drives a car from Y station towards X station at speed 60 kmh^–1. If he starts at the moment when one of the cars leaves station X, how many cars would be meet on route?

A stone is dropped from the top of a tower and travels 24.5 m in last second of its journey. The height of the tower is

A balloon starts rising from the ground with an acceleration of 1.25 m/s². After 8 s. stone is released from the balloon. The stone will

The velocity time graph of a body is shown in the Fig. The ratio of the average velocity during the intervals OC and CB is

A point initially at rest moves along the X – axis. Its acceleration varies with time as a = (5t + 6) m/s². If it starts from the origin, the distance covered by it in 2 second is

The time is expressed as function of x where α and β are constants as t = αx² + βx and υ is velocity. The retardation is

The motor of an electric train can give it an acceleration of 1 m/s² and brakes can give a negative acceleration of 3 m/s². The shortest time in which the train can make a trip between the two stations 1215 m apart is

A ball is dropped from top of a building. The ball takes 0.5s to fall past the 3m length of a window some distance from top of building. With what speed does the ball pass the top of window?

Two bodies are thrown vertically upwards with their initial speeds in the ratio 2:3. Then the ratio of the maximum heights attained by them is