A-Level Maths: Mechanics Practice

A ball is thrown vertically upwards with speed 12 m/s. How long does it take to return to its starting point? (Take g = 9.8 m/s²)

A velocity-time graph consists of a straight line from (0,0) to (4,8) then a horizontal line to (8,8). Find the total distance travelled.

A projectile is launched at 20 m/s at an angle of 30° to the horizontal. Find the maximum height reached. (g = 9.8 m/s²)

A 5 kg block on a rough horizontal surface is pushed by a horizontal force of 30 N. If the coefficient of friction is 0.4, find the acceleration. (g = 9.8 m/s²)

Two particles of mass 3 kg and 5 kg are connected by a light inextensible string passing over a smooth pulley. Find the acceleration of the system. (g = 9.8 m/s²)

A particle of mass 2 kg is placed on a smooth plane inclined at 30° to the horizontal. Find the acceleration down the plane. (g = 9.8 m/s²)

A car of mass 1200 kg accelerates from rest to 25 m/s. How much work is done by the engine? (Ignore resistive forces.)

A 2 kg object is released from rest at a height of 10 m. Find its speed just before it hits the ground, using energy conservation. (g = 9.8 m/s²)

A motor lifts a 200 kg load through a height of 15 m in 10 s. What is the power output of the motor? (g = 9.8 m/s²)

A uniform rod AB of length 3 m and mass 8 kg is pivoted at A. A force of 60 N is applied vertically upwards at B. Find the magnitude of the reaction at the pivot. (g = 9.8 m/s²)

A non-uniform plank AB of length 4 m and mass 20 kg is supported at A and at a point C, 1 m from B. The reaction at A is 120 N. Find the distance of the centre of mass from A. (g = 9.8 m/s²)

A uniform ladder of length 5 m and mass 15 kg rests against a smooth vertical wall with its base on rough horizontal ground. The ladder makes an angle of 65° with the ground. Find the minimum coefficient of friction at the ground. (g = 9.8 m/s²)

A 3 kg ball moving at 5 m/s collides with a stationary 2 kg ball. After the collision, the 3 kg ball moves at 2 m/s in the same direction. Find the velocity of the 2 kg ball.

A 4 kg object experiences an impulse of 24 Ns. If it was initially moving at 3 m/s, find its final velocity.

Two particles of equal mass m collide head-on with speeds u and 2u respectively. After the collision they move in opposite directions. If the collision is elastic, find the final speeds.

A 6 kg block is placed on a rough plane inclined at 35° to the horizontal. The coefficient of friction is 0.3. Find the acceleration if the block is released from rest. (g = 9.8 m/s²)

Two masses of 4 kg and 6 kg are connected by a string over a smooth pulley on an incline. The 4 kg mass hangs vertically and the 6 kg mass is on a smooth plane at 30°. Find the acceleration.

A force of F = (3i + 4j) N acts on a particle of mass 2 kg initially at rest. Find the magnitude of the velocity after 3 seconds.