Question Bank Directory

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx⁻²ⁿ where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by:

A ball is thrown vertically downwards with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with the velocity of 80 m/s. The height of the tower is: (assuming g = 10 m/s²)

If a body A of mass $M$ is thrown with a velocity $v$ at an angle of $30^{\circ}$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of $60^{\circ}$ to the horizontal. The ratio of horizontal range of A to B will be:

If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is:

A particle moves along a straight line OX. At a time t (in seconds), the displacement x (in metres) of the particle from O is given by x = 40 + 12t - t³. How long would the particle travel before coming to rest?

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of cross-sectional area $A$ of the wire is

The fundamental frequency of a closed organ pipe of a length $20 \text{ cm}$ is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

A stone falls under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂, and h₃ is:

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 ms⁻¹ while passing through a distance of 135 m in t seconds. The value of t is:

Dimensional formula of magnetic flux is:

The initial velocity of a particle is $10 \text{ m/sec}$ and its retardation is $2 \text{ m/sec}^2$. The distance moved by the particle in the 5th second of its motion is:

A bus is moving with a speed of 10 ms⁻¹ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what minimum speed should the scooterist chase the bus?

A stone falls freely under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂ and h₃ is:

Two bodies, A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is:

The displacement of a particle as a function of time is shown in the figure. The figure shows that

A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s, and (13 m, 14 m) at time t = 5 s. The average velocity vector v_avg from t = 0 to t = 5 s is:

A car moves from X to Y with a uniform speed vᵤ and returns to X with a uniform speed v_d. The average speed for this round trip is:

Velocity-time (v-t) graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is non-zero acceleration or retardation is:

The position of a particle with respect to time t along the x-axis is given by x = 9t² - t³ where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the +x-direction?

A particle moving along the x-axis has acceleration f, at time t, given by f = f₀(1 - t/T), where f₀ and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle’s velocity (vₓ) is: