Motion in a straight line

A particle, of mass $10^{-3}$ kg and charge 1.0 C, is initially at rest. At time $t = 0$, the particle comes under the influence of an electric field $\vec{E}(t) = E_0 \sin\omega t\, \hat{i}$, where $E_0 = 1.0\ \mathrm{N\,C^{-1}}$ and $\omega = 10^3\ \mathrm{rad\,s^{-1}}$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in $\mathrm{m\,s^{-1}}$, attained by the particle at subsequent times is ____________.

Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho}\frac{d\rho}{dt}\right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T = 0.01$ seconds and he measures the depth of the well to be $L = 20$ meters. Take the acceleration due to gravity $g = 10\ \mathrm{ms^{-2}}$ and the velocity of sound is $300\ \mathrm{ms^{-1}}$. Then the fractional error in the measurement, $\delta L/L$, is closest to

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as $t\to\infty$ is :

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s$^2$ and the car has acceleration 4 m/s$^2$. The car will catch up with the bus after a time of :

The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

A rocket is moving in a gravity free space with a constant acceleration of $2\ \mathrm{m\,s^{-2}}$ along $+x$ direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3\ \mathrm{m\,s^{-1}}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2\ \mathrm{m\,s^{-1}}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is

From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle, to hit the ground, is $n$ times that taken by it to reach the highest point of its path.

The relation between $H$, $u$ and $n$ is :

The phase space diagram for a ball thrown vertically up from ground is

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as [Take $g=10\ \mathrm{m/s^2}$.]

Column I describes some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situations in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.