Motion · Physics · MHT CET

At any time ' $t$ ', the co-ordinates of moving particle are $x=a t^2$ and $y=b t^2$. The speed of the particle is

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the $n^{\text {th }}$ second of its motion to the total distance travelled in n second is

The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance travelled by the body in time 0 to 8 s is

Two bodies A and B move in same straight line starting from same position. Body moves with constant velocity ' u ' and body B moves with constant acceleration ' $a$ '. When their velocities become equal, the distance between them is

A force acting on a body of mass 5 Kg is $(4 \hat{i}-2 \hat{j}+3 \hat{k}) \mathrm{N}$. If the body is initially at rest then the magnitude of its velocity at the end of 10 second in $\mathrm{m} / \mathrm{s}$ will be

A body travelling with uniform acceleration crosses two points A and B with velocities $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$ respectively. The speed of the body at mid point of A and B is (nearly)

The co-ordinates of a moving particle at any time ' $t$ ' are given by $x=\alpha t^3$ and $y=\beta t^3$ where $\alpha$ and $\beta$ are constants. The speed of the particle at time ' $t$ ' is given by

A ball is released from the top of a tower of height Hm . It takes T second to reach the ground. The height of the ball from the ground after $\frac{T}{4}$ second is

Two cars start from a point at the same time in a straight line and their positions are represented by $x_1(t)=a t+b t^2$ and $x_2(t)=F t-t^2$. At what time do the cars have the same velocity?

A bullet is fired on a target with velocity V . Its velocity decreases from V to $\mathrm{V} / 2$. When it penetrates 30 cm in a target. Through what thickness it will penetrate further in the target before coming to rest?

For the velocity-time graph shown in the figure below, the distance covered by the body in last two second of its motion is ' $\mathrm{S}_1$ '. What is the ratio of ' $\mathrm{S}_1$ ' to the total distance covered by it

A vehicle runs on a straight road of length 'L'. It travels half the distance with speed V and the remaining distance with speed $\frac{\mathrm{V}}{3}$. Its average speed is

The following figures show the variation of displacement with time of a particular object.

A velocity - time graph of a body is shown below. The distance covered by the body from 6 second to 9 second is

The ratio of weight of a man in a stationery lift and weight when the lift is moving downward with a uniform acceleration ' $a$ ' is $3: 2$. Then the value of ' $a$ ' is

For a projectile, the maximum height and horizontal range are same. The angle of projection ' $\theta$ ' of the projectile is

Which of the following person is in an inertial frame of reference?

A driver applies the brakes on seeing the red traffic signal 400 m ahead. At the time of applying brakes, the vehicle was moving with $15 \mathrm{~m} / \mathrm{s}$ and retarding at $0.3 \mathrm{~m} / \mathrm{s}^2$. The distance covered by the vehicle from the traffic light one minute after application of brakes is

The acceleration of a moving body can be found from

The position '$$x$$' of a particle varies with a time as $$x=a t^2-b t^3$$ where '$$a$$' and '$$b$$' are constants. The acceleration of the particle will be zero at

Two bodies $$A$$ and $$B$$ start from the same point at the same instant and move along a straight line. body $$A$$ moves with uniform acceleration $$a$$ and body $$B$$ moves with uniform velocity $$v$$. They meet after time $$t$$. The value of $$t$$ is

A small steel ball is dropped from a height of $$1.5 \mathrm{~m}$$ into a glycerine jar. The ball reaches the bottom of the jar $$1.5 \mathrm{~s}$$ after it was dropped. If the retardation is $$2.66 \mathrm{~m} / \mathrm{s}^2$$, the height of the glycerine in the jar is about (acceleration due to gravity $$g=9.8 \mathrm{~m} / \mathrm{s}^2$$ )

A large number of bullets are fired in all directions with same speed '$$U$$'. The maximum area on the ground on which the bullets will spread is

Which one of the following statements is Wrong?

A ball is projected vertically upwards from ground. It reaches a height '$$h$$' in time $$t_1$$, continues its motion and then takes a time $$t_2$$ to reach ground. The height $h$ in terms of $$g, t_1$$ and $$\mathrm{t}_2$$ is $$(\mathrm{g}=$$ acceleration due to gravity)

Two cars A and B start from a point at the same time in a straight line and their positions are represented by $$\mathrm{R}_{\mathrm{A}}(\mathrm{t})=$$ at $$+\mathrm{bt}^2$$ and $$\mathrm{R}_{\mathrm{B}}(\mathrm{t})=x \mathrm{t}-\mathrm{t}^2$$. At what time do the cars have same velocity?

A bullet is fired on a target with velocity '$$\mathrm{V}$$'. Its velocity decreases from '$$\mathrm{V}$$' to '$$\mathrm{V} / 2$$' when it penetrates $$30 \mathrm{~cm}$$ in a target. Through what thickness it will penetrate further in the target before coming to rest?

Two trains, each $$30 \mathrm{~m}$$ long are travelling in opposite directions with velocities $$5 \mathrm{~m} / \mathrm{s}$$ and $$10 \mathrm{~m} / \mathrm{s}$$. They will cross after

A body is released from the top of a tower '$$\mathrm{H}$$' metre high. It takes $$t$$ second to reach the ground. The height of the body $$\frac{t}{2}$$ second after release is

A shell is fired at an angle of $$30^{\circ}$$ to the horizontal with velocity $$196 \mathrm{~m} / \mathrm{s}$$. The time of flight is

$$\left[\sin 30^{\circ}=\frac{1}{2}=\cos 60^{\circ}\right]$$

A student is throwing balls vertically upwards such that he throws the $$2^{\text {nd }}$$ ball when the $$1^{\text {st }}$$ ball reaches maximum height. If he throws balls at an interval of 3 second, the maximum height of the balls is $$\left(\mathrm{g}=10 \frac{\mathrm{m}}{\mathrm{s}^2}\right)$$

A driver applies the brakes on seeing the red traffic signal $$400 \mathrm{~m}$$ ahead. At the time of applying the brakes, the vehicle was moving with $$15 \mathrm{~m} / \mathrm{s}$$ and retarding at $$0.3 \mathrm{~m} / \mathrm{s}^2$$. The distance covered by the vehicle from the traffic light 1 minute after the application of brakes is

A body at rest falls through a height 'h' with velocity 'V'. If it has to fall down further for its velocity to become three times, the distance travelled in that interval is

A bomb is dropped by an aeroplane flying horizontally with a velocity $$200 \mathrm{~km} / \mathrm{hr}$$ and at a height of $$980 \mathrm{~m}$$. At the time of dropping a bomb, the distance of the aeroplane from the target on the ground to hit directly is $$\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right)$$

A cricket player hit a ball like a projectile but the fielder caught the ball after 2 second. The maximum height reached by a ball is (g = 10 m/s²)

Two bodies '$$\mathrm{A}$$' and '$$\mathrm{B}$$' start from the same point at the same instant and move along a straight line. 'A' moves with uniform acceleration (a) and 'B' moves with uniform velocity (V). They meet after time 't'. The value of 't' is

A moving body is covering distances which are proportional to square of the time. Then, the acceleration of the body is