Practice Paper Mechanics 1 (Edexcel International A Level Maths: Pure 4)

A train leaves station , from rest with constant acceleration  later it passes a signal at which point the train decelerates uniformly until coming to rest at station X 75 seconds later.

Find the distance between station  and station .

The train then leaves station X  but travels in the opposite direction with constant acceleration . The train does not stop at station O but  after leaving station X  it passes a signal indicating that station Y  is 850 m away. At this point the train decelerates uniformly so it comes to rest at station Y.

Find the distance between station O and station Y

A particle of mass 3 kg starts from rest and is acted upon by three forces,  given in vector form as

where is a constant. The resultant of forces  is .

Given that  acts on a bearing of :

Find the value of the constant .

Work out the magnitude of the acceleration of the particle.

Find the total distance travelled by the particle in the first 4 seconds of its motion.

In a warehouse a hydraulic lift is being used to raise a large crate as shown in the diagram below:

The crate has a mass of 1200 kg and the platform of the lift has a mass of 300 kg. The lifting force is transmitted to the platform by means of a vertical rod of negligible mass.

Starting from rest, the platform and crate are accelerated vertically upwards at a constant rate so that they reach a velocity of 3 m s^-1 after 2 seconds.

Find the thrust in the rod.

Find the force exerted by the crate on the lifting platform.

Starting from rest a toy boat experiencing a constant acceleration of  takes 12 seconds to sail across a pond. Find the distance the toy boat sails across the pond, giving your answer to three significant figures.

A particle moves under constant acceleration . In a 6 second time period, the particle has initial velocity  and final velocity  where  and are constants.

Show that 

Find the values of  and .

A particle of mass 15 kg is sliding down a rough slope that is angled 25° to the horizontal. The coefficient of friction between the particle and the slope is 0.3.

Calculate the frictional force between the particle and the slope.

Hence calculate the acceleration of the particle down the slope.

A particle is being pulled up a smooth slope by a force of 60 N that acts at an angle of to the slope. The slope is inclined at  to the horizontal, as shown in the diagram below:

The particle experiences an acceleration of 0.3 m s^-2 parallel to the slope in the upwards direction.

Use the information provided above to calculate the mass of the particle.

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

 is a triangular lamina in which angle  is a right angle, and the lengths of sides  and are 58 cm and 42 cm respectively. Three forces are applied to the lamina at points  as shown in the diagram below:

Calculate the resultant moment of the three forces about point .

is a non-uniform rod of mass 10 kg and length 3 m.  rests horizontally on two supports placed at points  and , where  as shown in the diagram below:

Esmerelda attaches a 9 kg mass to the rod at a point 0.4 m to the left of , and measures the reaction force at . She then removes the mass and reattaches it to the rod at a point 0.4 m to the right of , and again measures the reaction force at . She finds that in her second measurement the reaction force at  is only one third the size of the reaction force at  in her first measurement.

By modelling the attached mass as a particle, use the above information to determine the position of the centre of mass of rod . Give the position in your answer as the distance of the centre of mass from point .

A TV camera runs along a horizontal track next to the pitch at a football match. The pitch is  long and the camera is initially positioned at the halfway line. The camera moves from rest at a constant velocity and after 6 seconds has displacement .

It then moves back to the halfway line at a constant velocity, taking 12 seconds to do so. For the next 6 seconds the camera moves with constant velocity .

Sketch a displacement-time graph to illustrate the motion of the camera.

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  seconds.

Write down the times at which the snooker ball hits a cushion and hence, find the length of the snooker table.

Show that the snooker ball comes to rest in exactly the same place it was struck from.