Practice Paper Mechanics 1 (Edexcel International A Level Maths: Pure 2)

Two particles,  and , with masses  and  respectively are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of is and the speed of is . Immediately after the collision, the speed of is  and the speed of  is .

The direction of motion of is reversed after the collision.

Show that .

State whether the direction of motion of  is reversed after the collision.

Given that  is double , find the values of  and .

To crash test cars, a computer‑controlled car is accelerated along a horizontal track and crashed into a wall. The maximum length of track available is 1.1 km long.

During a crash test, of track is required to increase a car’s speed from rest to . From this point onwards a car is accelerated at a constant rate. This is set to but can be varied up or down by 30% prior to a test being carried out.

Find the acceleration of a car during the first 20 m of a crash test.

Determine if it is possible to crash test a car at a speed of .

A crash test is unreliable if it takes under 10 seconds.
Find the lowest speed, in kilometres per hour, a car can be reliably crash tested at.

Jenna takes her two dogs Gamma and Omega for a walk in the park. Both dogs slip their leads and run off in different directions. When they stop, Gamma’s displacement from Jenna is , Omega’s displacement from Jenna is To collect the dogs Jenna walks at a constant speed directly to one dog then the other.

Jenna must decide which order to collect the dogs so that they are both retrieved as quickly as possible.

A particle of mass 0.9 kg is at rest on a rough horizontal plane.  A force of magnitude P N is acting on the particle at an angle of 40° to the horizontal.

Given that the coefficient of friction between the plane and the particle is 0.3, and that the particle is on the point of moving to the right under the influence of the force, find the value of P.

A particle of mass 12 kg is being pushed up a smooth slope by a force of 50 N that acts horizontally. The slope is inclined at  to the horizontal, as shown in the diagram below:

Calculate the acceleration of the particle up the slope.

Calculate the normal reaction force of the slope on the particle.

A snooker ball is struck such that it travels in a straight line up and down a snooker table. The graph below shows the velocity of the ball, , at time  after being struck.

When the snooker ball comes to rest it has displacement 0.3 m. Find the value of T and the total distance travelled by the ball.