Motion in a straight line practice · Mixed difficulty

Velocity of a body on reaching the point from which it was projected upwards, is

A ball thrown vertically upwards with an initial velocity of 1.4 m/s in 2s. The total displacement of the ball is

Statement I : Two objects moving with velocities $v_1$ and $v_2$ in the opposite directions, have their relative velocity along the direction of the one with a larger velocity.

Statement II : The relative velocity between two bodies moving with velocity $\mathbf{v}_1$ and $\mathbf{v}_2$ in same direction is given by $\mathbf{v}=\mathbf{v}_1-\mathbf{v}_2$

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

A room has dimensions $3\,m \times 4\,m \times 5\,m$. A fly starting at one comer ends up at the diametrically opposite conner. The magnitude of the displacement of the fly is

Essential characteristic of equilibrium is

A particle starts from rest, acceleration at $2\;m/{s^2}$ for 10 s and then goes with constant speed for 30 s and then decelerates at $4\;m/{s^2}$ till it stops. What is the distance travelled by it

If $a = 3{t^2} + 2t$ initial velocity is 5 m/s. Find the velocity at $\,t = 4\,s$. The motion is in straight line, $a$ is acceleration in $m/{s^2}$ and $t$ is time in seconds.

The relation $3t = \sqrt 3 x + 6$ describes the displacement of a particle in one direction, where x is in meter and t in second. The displacement when velocity is zero

A ball is dropped on the floor from a height of 10m. It rebounds to a height of 2.5m. If the ball is in contact with the floor for 0.01 s, the average acceleration during contact is nearly [Take $\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}$]

The distance travelled by a particle is directly proportional to $\sqrt{t}$, where $t$ is time elapsed. Which of the following is correct regarding the motion of the particle?

A train is moving slowly on a straight track with a constant speed of $2 \mathrm{~m} \mathrm{~s}^{-1}$. A passenger in that train starts walking at a steady speed of $2 \mathrm{~m} \mathrm{~s}^{-1}$ to the back of the train in the opposite direction of the motion of the train. So, to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be

If a body is moving along a straight path then which of the following is true?

The driver of a car moving with a speed of $10\mathrm{m}{\mathrm{s}^{ - 1}}$ sees a red light ahead, applies breaks and stops after covering 10m distance. If the same car were moving with a speed of $20\mathrm{m}{\mathrm{s}^{ - 1}}$, the same driver would have stopped the car after covering 30 m distance. Within what distance the car can be stopped if travelling with a velocity of $15\mathrm{m}{\mathrm{s}^{ - 1}}$? Assume the same reaction time and the same deceleration in each case.

Acceleration of a particle changes when

A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5m, the number of ball thrown per minute is (take $g = 10\;m{s^{ - 2}}$)

A hall has dimensions $10\,m \times 12\,m \times 14\,m$. A fly starting at one corner ends up at a diagonally opposite corner what is the magnitude of distance if it travels along three edges of hall

The average acceleration vector for a particle having a uniform circular motion is

Three ships A, B and C are in motion. The motion of A as seen by B is with speed V towards the north-east. The motion of B as seen by C is with speed V towards the north-west. Then, as seen by A, C will be moving towards the

Assertion: The relative velocity between any two bodies moving in opposite direction is equal to sum of the
velocities of two bodies.

Reason: Sometimes relative velocity between two bodies is equal to difference in velocities of the two.

A ball P is dropped vertically and another ball Q is thrown horizontally with the same velocities from the same height and at the same time. If air resistance is neglected, then

A bullet is fired with a speed of 1000 m/sec in order to hit a target 100 m away. If $g = 10\;m/{s^2}$, the gun should be aimed

When acceleration be function of velocity as $a=f(v)$, then

A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is

A body falls from a height h=200m (at New Delhi). The ratio of distance travelled in each 2 sec during t=0 to t=6 second of the journey is

A ball is thrown vertically upwards from the top of a tower of height h with velocity v. The ball strikes the ground after

A particle covers equal distance around a circular path, in equal intervals of time. Which of the following quantities connected with the motion of the particle remains constant with time?

The numerical ratio of displacement to distance is

If an object is falling freely in vacuum, then body moves with

Position of particle during motion is expressed as $\vec r = \left( {5{t^2}\hat i + 3t\,\hat j} \right)m$. The magnitude of acceleration of particle at t = 0, is