Motion In A Straight Line

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

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_P = at + bt^2$ and $x_Q = ft - t^2$. At what time do the cars have the same velocity?

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:

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force qE, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively:

A person in a lift drops a coin. The coin takes time $t_1$ to reach the floor when the lift is at rest, and time $t_2$ when the lift is moving up with uniform velocity. Then:

A person travelling in a straight line moves with a constant velocity $v_1$ for a certain distance x and with a constant velocity $v_2$ for the next equal distance. The average velocity v is given by the relation:

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is (g = 10 m/s$^2$):

A small block slides down from the top of a smooth inclined plane starting from rest at t = 0. If $S_n$ is the distance travelled by it from t = (n-1) s to t = n s, the ratio $\dfrac{S_n}{S_{n+1}}$ is:

The displacement-time (x-t) graphs of two moving particles make angles of 30° and 45° with the time axis as shown. The ratio of their respective velocities $v_1 : v_2$ is:

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

A ball is thrown vertically upward with a velocity of 4 m/s from a bridge. The ball strikes the water surface after 4 s. The height of the bridge above the water surface is (g = 10 m/s$^2$):

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

A bullet enters a wooden block with speed u and, after travelling 24 cm inside it, its speed reduces to u/3. Assuming uniform retardation, the further distance it travels before coming to rest is:

The velocity (v)-time (t) graph of a body moving in a straight line is shown. Which of the following acceleration (a)-time (t) graphs best represents the motion?

Buses leave cities X and Y in both directions at regular intervals of T minutes with the same speed. A girl driving from X to Y at 60 km/h notices that a bus moving in her direction passes her every 30 min, while a bus moving in the opposite direction passes her every 10 min. The interval T and the speed of the buses are respectively:

The relation between time t and position x of a particle moving along a straight line is given by $t = x^2 + x$. The acceleration of the particle is:

A particle moves along a straight line with position $s(t)=\alpha t^2-\beta t+\gamma$, where $\alpha=1\,\text{ms}^{-2}$, $\beta=6\,\text{ms}^{-1}$, $\gamma=5\,\text{m}$. The average speed of the particle (in $\text{ms}^{-1}$) from $t=0$ to $t=6\,\text{s}$ is:

A ball is thrown vertically upward and falls back to the thrower. Which velocity (v)-time (t) graph correctly represents its motion? (upward taken positive)

A ruler is dropped vertically and five persons try to catch it. Their reaction times are A = 0.20 s, B = 0.22 s, C = 0.18 s, D = 0.19 s and E = 0.21 s. The correct order of the distance travelled by the ruler before being caught by each person is: