The acceleration of a particle starting from rest varies with time according to the relation A = – aω²sinωt. The displacement of this particle at a time t will be:

If the velocity of a particle is (10 + 2t²) m/s, then the average acceleration of the particle between 2 sec and 5 sec is:

A thief is running away on a straight road in a jeep moving with a speed of 9 ms^–1. A policeman chases him on a motor cycle moving at a speed of 10 ms^–1. If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the policeman to catch the thief?

A car A is travelling on a straight level road with a uniform speed of 60 km/h. It is followed by another car B which is moving with a speed of 70 km/h. When the distance between them is 2.5 km, the car B is given a deceleration of 20 km/h². After how much time will B catch up with A

The speed of a body moving with uniform acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their acceleration are 0.3 m/s² and 0.2 m/s² respectively, then the time they take to pass each other will be

A body starts from rest with uniform acceleration. If its velocity after n second is v, then its displacement in the last two seconds is

A particle is moving in a straight line and passes through a point O with a velocity of 6 ms^–1. The particle moves with a constant retardation of 2 ms^–2 for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

A particle is projected with velocity $v_0$ along x-axis. The deceleration of the particle is proportional to the square of the distance from the origin i.e., $a=\alpha x^2.$ The distance at which the particle stops is :

A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are

A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4h. The two stones cross each other after time:

Four marbles are dropped from the top of a tower one after the other with a one-second interval. The first one reaches the ground after 4 seconds. When the first one reaches the ground the distances between the first and second, the second and third and the third and fourth will be, respectively:

Two bodies are thrown simultaneously from a tower with same initial velocity v₀ : one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is

A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is:

A particle is projected upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂ respectively. The velocity of projection will be:

A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity u.

Two cars are moving in the same direction with the same speed 30 km/hr. They are separated by a distance of 5 km. The speed of a car moving in the opposite direction, if it meets these two cars at an interval of 4 minutes, will be

A 150 m long train is moving to north at a speed of 10 m/s. A parrot flying towards south with a speed of 5 m/s crosses the train. The time taken by the parrot the cross to train would be: 

A moves with 65 km/h while B is coming back of A with 80 km/h. The relative velocity of B with respect to A is 

Two trains along the same straight rails moving with constant speed 60 km/hr and 30 km/hr respectively towards each other. If at time t = 0, the distance between them is 90 km, the time when they collide is:

A bus is moving with a velocity 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus

An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e. 120 km/h, the stopping distance will be 

A lift is going up. The total mass of the lift and the passenger is 1500 kg. The variation in the speed of the lift is as given in the graph. The height to which the lift takes the passenger is

An iron ball and a wooden ball of the same radius are released from a height ‘h’ in a vacuum. The time taken by both of them to reach the ground is

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_p\left(t\right)=at+b{t}^2$ and $x_Q\left(t\right)=ft-t^2$. At what time do the cars have the same velocity?

If the velocity of a particle is $\mathrm{v}=\mathrm{At}+{\mathrm{Bt}}^2$, where A and B are constants, then the distance travelled by it between 1s and 2s is?

$$\begin{gathered} 1. 3\mathrm{A}+7\mathrm{B} \\ 2. \frac{3\mathrm{A}}{2}+\frac{7\mathrm{B}}{3} \\ 3. \frac{\mathrm{A}}{2}+\frac{\mathrm{B}}{3} \\ 4. \frac{\mathrm{A}}{3}+\frac{\mathrm{B}}{2} \end{gathered}$$

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x)=$\beta x^{-2n}$ where, $\beta$ and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by

A stone falls under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h_2, and h₃ is

The motion of a particle along a straight line is described by equation

where x is in metre and t is in second. The retardation of the particle when its velocity becomes zero is

                        $x=8+12t-t^3$

A boy standing at the top of a tower of 20 m height drops a stone. Assuming g=$10 {\mathrm{ms}}^{-2}$, the velocity with which it hits the ground will be