Motion in a straight line practice · Medium

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

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.

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?

From the top of a tower, a stone is thrown up and reaches the ground in time ${t_1} = 9\mathrm{s}.$. A second stone is thrown down with the same speed and reaches the ground in time ${t_2} = 4$ s. A third stone is released from rest and reaches the ground in time ${t_3}$, which is equal to

The velocity of a particle depends upon the time $\mathrm{t}$ according to the equation: $\mathrm{v}=\sqrt{\mathrm{a b}}+\mathrm{b t}+\frac{\mathrm{c}}{\mathrm{d+t}}$. The physical quantities which are represented by $\mathrm{a, b, c}$ and $\mathrm{d}$, are in the following order:

Can an object maintain uniform velocity when its acceleration is not zero?

A body travels a distance $s_1$ with velocity $v_1$ and distance $s_2$ with velocity $v_2$ in the same direction. Calculate the average velocity of the body:

A ball kicked vertically up attains a height of 19.6m and returns to the point of throw. If the ball is in air for four second, then the value of acceleration due to gravity is

The position vector of particle changes with time according to the relation $r(t) = 15{t^2}\hat i + (4 - 20{t^2})\hat j$. What is the magnitude of the acceleration (in $m{s^{ - \mathrm{2}}}$) at t =1 ?

A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then