Two cars, A and B, start from rest at the same point. Car A moves with constant acceleration 'a' and car B moves with constant acceleration '2a'. After how much time will the distance between them be 'S'?

An object's motion in the x-y plane is given by $\vec r = 3\cos \left( {2t} \right)\hat x + 3\sin \left( {2t} \right)\hat y$. What is the radius of the object's trajectory?

The displacement of a particle varies according to the relation x=4(cos⁡πt+sin⁡πt). The amplitude of the particle is

A body describes $SHM$ with an amplitude of $50\,cm$ and a time period of 1.57 seconds. The velocity of the body when its displacement becomes $30\,cm$ is

A particle of 0.25 kg vibrates with a period of 2 second. If its greatest displacement is 0.4 m the maximum velocity in $m{s^{ - 1}}$ is

A horizontal platform vibrates with simple harmonic motion in the horizontal direction with a period 2 s. A body of mass 0.5 kg is placed on the platform. The coefficient of static friction between the body and platform is 0.3. What is the maximum frictional force on the body when the platform is oscillating with amplitude 0.2 m? Assume ${\pi ^2} = 10 = g$.

A S.H.M. has amplitude $'a'$ and time period $T$.The maximum velocity will be

A particle completes one full cycle of SHM in 2 seconds. If its amplitude is 5 cm, what is its average velocity over this period?

A large horizontal surface moves up and down in SHM with an amplitude of 1 cm. if a mass of 10 kg (which is placed on the surface) is to remain continuously is in contact with it. The maximum frequency of SHM will be

A simple pendulum performs simple harmonic motion about $\;X = 0$ with an amplitude A and time period $T$. The speed of the pendulum at $X = \frac{A}{2}$ will be

A particle moves in the x-y plane with its position vector given by $\vec{R} = 4\sin(\pi t)\hat{i} + 4\cos(\pi t)\hat{j}$, where R is in meters and t is in seconds. Which of the following is incorrect?