Motion in a straight line practice · Mixed difficulty

The motion of a particle along a straight line is described by equation $x=2+12 t-t^2$, where $x$ is in metre and $t$ is in second. The retardation of the particle when its velocity becomes zero is

In a race for 100m dash, the first and the second runners have a gap of one metre at the mid way stage. Assuming the first runner goes steady, by what percentage should the second runner increases his speed just to win the race.

Speed is in general _____ in magnitude than that of the velocity.

A body starts from rest, the ratio of distances travelled by the body during $3^{\text {rd }}$ and $4^{\text {th }}$ second is:

Assertion: A negative acceleration of a body can be associated with a ‘speeding up’ of the body.

Reason: Increase in speed of a moving body is independent of its direction of motion.

Choose the wrong statement from the following.

A 150 m long train is moving with a uniform velocity of 45 kmph. The time taken by the train to cross a bridge of length 850 m is

A juggler throws balls into air. The throws one whenever the previous one is at its highest point. If the throws n balls each second, the height to which each ball will rise is

If a particle travels $n$ equal distances with speeds $v_1, v_2, \ldots, v_n$ then the average speed $\bar{V}$ of the particle will be such that

A scooter accelerates from rest for time ${t_1}$ at constant rate ${a_1}$ and then retards at constant rate ${a_2}$ for time ${t_2}$ and comes to rest. The correct value $\frac{{{t_1}}}{{{t_2}}}$ of will be

A burglar's car had a start with an acceleration of $2 \mathrm{~ms}^{-2}.$ A police vigilant party came after 5 seconds and continued to chase the burglar's car with a uniform velocity of $20 \mathrm{~ms}^{-1}.$ Find the time in which the police van overtakes the burglar's car.

Which of the following are true?
(i) A body having constant speed can have verying velocity.
(ii) Position-time graphs for two objects with zero relative velocity are parallel.
(iii) The numerical ration of velocity to speed of an object can never be more than one.

A graph is shown between velocity an time for the motion of a particle. The area under the curve between the time intervals ${t_1}\,and\,{t_2}$ gives

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

From a height, 3 balls are thrown with speed $u$, one vertically upward, second horizontally, third downward with times of fall be $t_1, t_2$ and $t_3$ respectively, then

What is the numerical ratio of velocity to speed of an object?

Assertion: If two particles are moving with same speed but their velocity vectors are opposite, then the distance between the particles must be changing.
Reason: If the velocity of one particle w.r.t. other is zero, then separation between the particle must be constant.

The distance traveled by a falling body in the last second of its motion, to that in the last but one second is 7:5. The velocity with which body strikes the ground is

Assertion: The position-time graph of a body moving uniformly in a straight line is parallel to position axis.
Reason: The position-time graph in a non-uniform motion gives constant velocity at all instants of time.

Assertion: Magnitude of average velocity is equal to average speed, if velocity is constant.
Reason: If velocity is constant, then there in no change in the direction of motion.

A truck and a car are moving with equal velocity. On applying the brakes both will stop after certain distance, then

When particle moves in straight line increasing speed the correct sign of acceleration '$a$' and velocity '$v$' can be

Assertion: The speed of an object can never be negative.
Reason: Speed is a scalar quantity.

Which of the following statements is true for a car moving on the road?

If a particle moves with an acceleration, then which of the following can remain constant

If a particle is moving along a straight line and its velocity varies with time, as $v=2 t-t^2$, ( $v$ and $t$ are in $\mathrm{SI}$ units) then choose the incorrect option.

A body A moves with uniform acceleration A and Zero initial velocity, Another body B, starts from the same point moves in the same direction with a constant velocity V.
The two bodies meet after a time t. The value of t is

The displacement of a particle undergoing rectilinear motion along the x-axis is given by $x = \left( {2{t^3} + 21{t^2} + 60t + 6} \right)$. The acceleration of the particle when its velocity is zero is

Assertion: A body moving with constant acceleration, always travels equal distance in equal time intervals.
Reason: Motion of the body with constant acceleration is a uniform motion.

A passenger is standing on the platform at the beginning of the $n^{\text {th }}\left(=3^{\text {rd }}\right)$ coach of a train. The train starts moving with constant acceleration. The third coach passes by the passenger in $\Delta t_1=5.0 \mathrm{~s}$ and rest of the train (including the $3^{\text {rd }}$ coach) in $\Delta t_2=20 \mathrm{~s}$. In what time interval $\Delta t$ (in sec) did the last coach passed by the passenger?