Engineering Mec...

A particle moves in a straight line and its position is defined by equation $x=6t^2-t^3$ where t is expressed in seconds and x in meters. The maximum velocity(m/s) during motion is____

A horizontal circular platform of radius 1m and mass 0.6 kg is free to rotate about its axis. Two massless guns, each carrying a bullet of mass 65 gm are attached at a distance of 0.4 m and 0.6 m from center and in opposite direction. If the guns fire simultaneously and speed of bullets are 25 m/s (each), then the magnitude of rotational speed of platform is

Two blocks of equal masses are made. One of them is smooth and the other is rough with coefficient of friction 0.20 with the floor. The smooth block is moving at 20 m/s towards the rough block at rest. If their collision is perfectly elastic, then the distance travelled by the rough block will be ______

A Train of length 500 m is travelling in 30° north east direction with a uniform acceleration of 0.2 m/s² and at t = 0, it has a speed of 54 kmph. At the same time (t = 0), a Benz car started from different location from rest and travelling in east direction with a uniform acceleration of 0.4 m/s². At t = 25 sec, a passenger sitting in Benz observed the train on his left side.

(Assume the angle is measured from east direction)

A bullet is fired from a gun. The force on the bullet is given by F = 600 – 2 × 10⁵ t where F is in newton and t in seconds. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

In an IPL match between MI and RCB, Chahal bowled a full toss delivery to Rohit, Rohit pulled it away for a maximum. The mass of the ball is 160 gms and the mass of the Rohit’s bat is 1.5 kg. The speed of ball is 90 kmph just before the hit and 144 kmph just after the hit. The bat swing speed just before hitting the ball is 54 kmph and the ball is in contact with the bat for 3 ms.

(Assume hitting the ball with bat as a 1D collision)

The motion of a particle moving along a curve is defined by y = x³- 3x + 150, starting with an initial velocity of $\overrightarrow{V_0}=3\hat{i}-14\hat{j}$ m/s. If V_x is constant, then which of the following statements are true at x = 5 m?