Kinematics · JEE Main previous year questions

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

1. A.$y=x^2+\text{constant}$
2. B.$y^2=x+\text{constant}$
3. C.$xy=\text{constant}$
4. D.$y^2=x^2+\text{constant}$

1. A.$13m/{\mathrm{s}}^2$
2. B.$12m/{\mathrm{s}}^2$
3. C.$7.2\mathrm{m}{\mathrm{s}}^2$
4. D.$14m/{\mathrm{s}}^2$

A motor cycle starts from rest and accelerates along a straight path at $2m/s^2$. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\%$ of its value when the motor cycle was at rest? (Speed of $\mathrm{sound}=330m{s}^{-1}$)

1. A.$98m$
2. B.$147m$
3. C.$196m$
4. D.$49m$

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

1. A.$t^2$
2. B.$t$
3. C.$t^{1/2}$
4. D.$t^3$

A ball of mass $0.2kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2m$ while applying the force and the ball goes upto $2m$ height further, find the magnitude of the force. (consider $g=10m/{\mathrm{s}}^2$).

1. A.$4N$
2. B.$16N$
3. C.$20N$
4. D.$22N$

A particle of mass $100g$ is thrown vertically upwards with a speed of $5m/s$. The work done by the force of gravity during the time the particle goes up is

1. A.$-0.5J$
2. B.$-1.25J$
3. C.$1.25J$
4. D.$0.5J$

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

1. A.$R^2$
2. B.$\frac{1}{R^2}$
3. C.$\frac{1}{R}$
4. D.$R$

A projectile can have the same range 'R' for two angles of projection. If $T_1$ and $T_2$ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

1. A.R
2. B.$\frac{1}{R}$
3. C.$\frac{1}{R^2}$
4. D.$R^2$

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

1. A.$x$
2. B.$e^x$
3. C.$x^2$
4. D.${\log }_{e}x$

The displacement $y$ of a particle in a medium can be expressed as, $y=10^{-6}\sin \left(100t+20x+\frac{\pi }{4}\right)\mathrm{m}$ where $t$ is in second and $x$ in meter. The speed of the wave is

1. A.$20m/s$
2. B.$5m/s$
3. C.$2000m/s$
4. D.$5\pi m/s$

From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the same speed ). If $v_A$ and $v_B$ are their respective velocities on reaching the ground, then

1. A.$v_B>v_A$
2. B.$v_A=v_B$
3. C.$v_A>v_B$
4. D.their velocities depend on their masses.

The maximum velocity (in $\mathrm{m}{\mathrm{s}}^{-1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction $0.6$ to avoid skidding is

1. A.$60$
2. B.$30$
3. C.$15$
4. D.$25$