Motion In One D...

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is

A body is slipping from an inclined plane of height h and length l. If the angle of inclination is θ, the time taken by the body to come from the top to the bottom of this inclined plane is

A particle moves with uniform acceleration along a straight line AB. Its velocities at A and B are 2 m/s and 14 m/s, respectively. M is the mid-point of AB. The particle takes t₁ seconds to go from A to M and t₂ seconds to go from M to B. Then t₂/t₁ is

A police party is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motorcycle. When he is at a distance x from the jeep, he accelerates from rest at a constant rate. Which of the following relations is true if the police are able to catch the dacoit?

A train is moving at a constant speed V when its driver observes another train in front of him on the same track and moving in the same direction with constant speed v. If the distance between the trains is x, then what should be the minimum retardation of the train so as to avoid collision?

A bird flies to and fro between two cars which move with velocities v₁ = 20 m/s and v₂ = 30 m/s. If the speed of the bird is v₃ = 10 m/s and the initial distance of separation between them is d= 2 km, find the total distance covered by the bird till the cars meet.

A man swimming downstream overcome a float at a point M After travelling distance D he turned back and passed the float at a distance of D/2 from the point M, then the ratio of speed of swimmer with respect to still water to the speed of the river will be

Two balls are dropped from the top of a high tower with a time interval of t_0​ second, where t₀​ is smaller than the time taken by the first ball to reach the floor, which is perfectly inelastic. The distance S between the two balls, plotted against the time lapse t from the instant of dropping the second ball, is best represented by

A particle is thrown up inside a stationary lift of sufficient height. The time off light is T. Now it is thrown again with same initial speed v₀ with respect to lift. At the time of
second throw, lift is moving up with speed v₀ and uniform acceleration g upward (the acceleration due to gravity). The new time of flight is