Kinematics Questions

A ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant a person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

An automobile travelling with speed of $60\text{km/h}$, can brake to stop within a distance of $20\text{m}$. If the car is going twice as fast, i.e $120\text{km/h}$, the stopping distance will be:

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of the ball in $T/3$ seconds?

A point mass oscillates along the $x$ -axis according to the law $x=x_0\cos (\omega t-\pi /4)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then:

The velocity of a particle is $v=v_0+gt+f{t}^2$. If its position is $x=0$ at $t=0$, then its displacement after unit time ($t=1$) is:

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2\times 10^{-2}\cos \pi t$ metres. The time at which the maximum speed first occurs is:

A particle located at $x=0$ at time $t=0$, starts moving along the positive $x$ -direction with a velocity $v$ that varies as $v=\alpha \sqrt{x}$. The displacement of the particle varies with time as:

A body falling from rest under gravity passes a certain point $P$. It was at a distance of $400\text{m}$ from $P$, $4\text{s}$ prior to passing through $P$. If $g=10{\text{m/s}}^2$, then the height above the point $P$ from where the body began to fall is:

A particle is projected at $60^{\circ }$ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is:

A body starts from rest at $x=0,t=0$ with constant acceleration $a$. Simultaneously another body passes $x=0$ with constant speed $v$. The position of the first is $x_1(t)$ and the second is $x_2(t)$. Which graph describes $(x_1-x_2)$ vs $t$?

Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$, respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal acceleration is:

A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after $10\text{s}$ is:

Consider a rubber ball freely falling from a height $h=4.9\text{m}$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as function of time will be:

A particle is moving with velocity $\vec{v}=K(y\hat{i}+x\hat{j})$, where $K$ is a constant. The general equation for its path is:

A point $P$ moves in counter-clockwise direction on a circular path of radius $20\text{m}$. The movement of '$P$ ' is such that it sweeps out a length $s=t^3+5$, where $s$ is in metres and $t$ is in seconds. The acceleration of '$P$ ' when $t=2\text{s}$ is nearly:

For a particle in uniform circular motion the acceleration $\vec{a}$ at a point $P(R,\theta )$ on the circle of radius $R$ is (here $\theta$ is measured from the $x$ -axis):

An object, moving with a speed of $6.25\text{m/s}$, is decelerated at a rate given by:
$$\frac{dv}{dt}=-2.5\sqrt{v}$$
where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be:

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$, the total area around the fountain that gets wet is:

A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F(t)=F_0{e}^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

A boy can throw a stone up to a maximum height of $10\text{m}$. The maximum horizontal distance that the boy can throw the same stone up to will be:

A lizard, at an initial distance of $21\text{ cm}$ behind an insect, moves from rest with an acceleration of $2{\text{ cm/s}}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20\text{ cm/s}$. Then the lizard will catch the insect after:

The co-ordinates of a moving particle at any time $t$ are given by $x=\alpha t^3$ and $y=\beta t^3$. The speed of the particle at time $t$ is given by:

A boy playing on the roof of a $10\text{m}$ high building throws a ball with a speed of $10\text{m/s}$ at an angle of $30^{\circ }$ with the horizontal. How far from the throwing point will the ball be at the height of $10\text{m}$ from the ground? (Take $g=10{\text{m/s}}^2$)

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to:

A car moving with a speed of $50\text{km/hr}$, can be stopped by brakes after at least $6\text{m}$. If the same car is moving at a speed of $100\text{km/hr}$, the minimum stopping distance is:

A body travels a distance $s$ in $t$ seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration $f$ and in the second part with constant retardation $r$. The value of $t$ is given by:

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $u$ and the other from rest with uniform acceleration $f$. Let $\alpha$ be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time:

A parachutist after bailing out falls $50\text{ m}$ without friction. When parachute opens, it decelerates at $2{\text{ m/s}}^2$. He reaches the ground with a speed of $3\text{ m/s}$. At what height, did he bail out?

A particle is moving eastwards with a velocity of $5\text{ m/s}$. In $10\text{ seconds}$ the velocity changes to $5\text{ m/s}$ northwards. The average acceleration in this time is:

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 $15S$, then:

The relation between time $t$ and distance $x$ is $t=a{x}^2+bx$ where $a$ and $b$ are constants. The acceleration is:

A projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to:

Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f^{\prime }$ respectively. If $A$ takes $m\text{ sec.}$ more than $B$ and describes $n$ units more than $B$ in acquiring the same speed then: