In some appropriate units, time (t) and position (x) relation of a moving particle is given by \(\text{t}\,=\,\text{x}^2\,+\,\text{x}\). The acceleration of the particle is

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction, Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

The velocity (v)− time (t) plot of the motion of a body is shown below:

The acceleration (a)− time (t) graph that best suits this motion is :

A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes u/3. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is

The ratio of the distances travelled by a freely falling body in the 1^st , 2^nd , 3^rd and 4^th second

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 ms⁻¹. The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g = 10m s⁻²)

The displacement-time graphs of two moving particles make angles of \(30^ \circ\) and \(45^ \circ\) with the x-axis as shown in the figure. The ratio of their respective velocity is

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let \(S_n\) be the distance travelled by the block in the interval \(t\, =\, n − 1\) to \(t\, =\, n\). Then, the ratio \(\displaystyle \frac{S_n}{S_{n+1}}\) is

A car starts from rest and accelerates at 5 m/s². At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s?(Take g = 10 m/s²)

A ball is thrown vertically downward with a velocity of 20m ∕ s from the top of a tower. It hits the ground after some time with a velocity of80m ∕ sThe height of the tower is : (g = 10m ∕ s²)

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\). On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk up on the moving escalator will be

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