Motion in a straight line practice · Mixed difficulty

A body starts moving from rest with constant acceleration covers displacement $S_1$ in first $(p-1)$ seconds and $S_2$ in first $p$ seconds. The displacement $S_1+S_2$ will be made in time:

A balloon starts rising from the ground with an acceleration of $1.25\,\,m\mathrm{/}{s^2}$ after 8 seconds, a stone released from the balloon, the stone will $[g = 10\,\,m\mathrm{/}{s^2}]$

Statement-1: Two balls of different masses are thrown vertically upwards with same speed. They will pass through their point of projection in the downward direction with the same speed in absence of air resistance.
Statement-2: In absence of air resistance, the mechanical energy of a projectile is conserved.

A drunkard takes a step of $1 \mathrm{~m}$ in 1 second. He takes 5 seconds steps forward and 3 seconds steps backwards, and so on. The time taken by him to fall in a pit $13 \mathrm{~m}$ away from the starts is

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

Stopping distance of a moving vehicle is directly proportional to

Assertion : A positive acceleration of a body can be associated with 'slowing down' of the body.

Reason : Acceleration is a vector quantity.

Assertion: If a particle is thrown upwards then distance travelled in last second of upward journey is independent of the velocity of projection.
Reason: In last second distance travelled is $4.9 \mathrm{~m}$. (take $g=9.8 \mathrm{~m} / \mathrm{s}^2$)

The distance $x$ (in $\mu {m}$ ) covered by a molecule starting from point ${A}$ at time ${t}=0$ and stopping at another point ${B}$ in given by the equation

$x=t^2\left(2+\frac{t}{3}\right)$

The distance between $A$ and $B$ (in $\mu {m}$ ) is closed to

A police jeep is chasing culprit going on motorcycle. The motorcycle crosses a turning at $20 \mathrm{~m} / \mathrm{s}$. The jeep follows at speed of $30 \mathrm{~m} / \mathrm{s}$, crossing the turning 6 second later than motor cycle. If they travel at constant speeds, how far from turning point jeep catches up the motorcycle?

A bird flies due south with velocity $30 {~m} / {s}$ for 10 ${s}$, it rests for $2 {~s}$ and then flies due north with velocity $32 {~m} / {s}$ for $8 {~s}$. The average velocity of the bird

(in ${m} / {s}$ ) for the whole trip is;

(Consider north direction along positive y axis.)

Assertion (A): Starting from rest with zero acceleration if acceleration of particle increases at a constant rate of $2 \mathrm{~ms}^{-3}$ then velocity should increase at constant rate of $1 \mathrm{~ms}^{-2}$.

Reason (R): For the given condition.

$\frac{d a}{d t} =2 \mathrm{~ms}^{-3}$

$a =2 t$

A cat wants to catch a rat. The cat follows the path whose equation is $x+y=0$, but the rat follows the path whose equation is $x^2+y^2=4$. The coordinates of possible points of catching the rat are

Assertion: For an object having uniformly accelerated motion, the position-time graph is parabolic in nature.

Reason: In a uniformly accelerated motion, the acceleration is constant.

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?

Two stones of masses $2 \mathrm{~kg}$ and $4 \mathrm{~kg}$ are dropped from height $30 \mathrm{~m}$ and $40 \mathrm{~m}$ respectively. The ratio of time taken by the stones to reach the ground is

Two balls are dropped from the top of a cliff at a time interval $\Delta t=2 \mathrm{~s}$. The first ball hits the ground, rebounds elastically (essentially reversing direction instantly without losing speed) and collides with the second ball at height $h=55 \mathrm{~m}$ above the ground. How high is the top of the cliff (in $\mathrm{m}$ )?

A particle moves along a straight line such that its displacement at any time $t$ given by

$s=\left(\frac{t^4}{2}-12 t^2\right) m$

The velocity when the acceleration becomes zero is

A body is moving with uniform acceleration covers 200 m in the first 2 s and 220 m in the next 4 s. find the velocity in $\mathrm{m}{\mathrm{s}^{ - 1}}$ after 7 s.

A train starts from rest and moves with a constant acceleration of $2.0 \mathrm{~m} / \mathrm{s}^2$ for half a minute. The brakes are then applied and the train comes to rest in one minute. Find (a) the total distance moved by the train, (b) the maximum speed attained by the train and (c) the position(s) of the train at half the maximum speed.

A person walks up a stalled escalator in $90 \mathrm{~s}$. When he is just standing on the same moving escalator, then he is carried for $60 \mathrm{~s}$. The time it would take him to walk up the moving escalator will be

A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30 m. Which of the following statement about the motion of the particle is false

Assertion : A body may be accelerated even when it is moving uniformly.

Reason : When direction of motion of the body is changing, the body must have acceleration.

If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest

The velocity of a body depends on time according to the equation $v=40+0.2 t^3$. The body is undergoing

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in $t\,s$, the distance travelled by the toy in the next $t\,s$ will be :

The position of a particle moving along $x$-axis varies with time $t$ as $x=4 t-t^2+1$. Find the time interval(s) during which the particle is moving along positive $x$-direction.

A point moves such that its displacement as a function of time is given by $x^3=t^3+1$. Its acceleration as a function of time $t$ will be

Assertion: The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.

Reason: Velocity is a vector quantity and speed is a scalar quantity.

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three second. The body has fallen for a time of:-