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

A particle is projected upwards from ground level with velocity  6 seconds later it has a velocity of . Find the value of u.

Find the displacement of the particle, from its initial position, 4 seconds later.

Melody is practising her skateboarding skills along a horizontal stretch of ground. She starts from rest and accelerates uniformly for 4 seconds at which point she has reached the speed . Melody then travels at this speed for 10 seconds. She then decelerates uniformly until she comes to rest which takes 5 seconds.

Sketch a velocity-time graph for the motion of the skateboard.

During the motion, Melody travels 174 metres.

Find the value of .

Sketch an acceleration-time graph for the motion of the skateboard.

A particle of mass 0.7 kg is on a rough plane which is angled at  to the horizontal.  The particle is being held at rest by a force of  N acting up the plane along the line of greatest slope.

Given that the coefficient of friction between the particle and the plane is 0.35, and that the particle is on the point of slipping up the plane, find the value of .

is a non-uniform rod of mass 12 kg and length 4 m.  is held horizontally in equilibrium by a support placed at point  and a vertical wire attached to point such that  and  as shown in the diagram below:

A weight of mass 15 kg is attached to the rod at point  and the rod is at the point of tilting about point .  The weight is then removed.

Find the ratio of the reaction force at  to the tension in the wire at when there are no external weights attached to the rod.  Give your answer in the form  where  and  are integers with no common factors other than 1.

The 15 kg weight is then attached to the rod between points  and .

Find the greatest distance to the left of point  that the weight can be attached without the rod beginning to tilt.

It takes three minutes for a particle to travel  with constant acceleration. The particle’s velocity at the start of the three minutes is half of its velocity at the end. Find the magnitude of the acceleration giving your answer as a fraction, in metres per square second.

Two forces  and  act on a particle, where  newtons and newtons.
 newtons.

The resultant force  acting on the particle is given by , and acts in a direction parallel to the vector .

Find the angle between  and the vector j, giving your answer in degrees correct to 2 decimal places.

Show that .

Given that , find the magnitude of R.

Two masses  and  are placed in a light scale-pan, with mass  resting on top of mass  as shown in the diagram below:

Mass  has a mass of  700 g  and mass  has a mass of  900 g.  The scale-pan is attached to a vertical light inextensible string.

Using the string, the scale-pan is raised vertically with an acceleration of

Find:

the tension in the string

the force exerted on mass  by mass 

the force exerted on mass  by mass 

the force exerted on mass  by the scale-pan.

A scientist has set up a device to measure the frictional resistance force between a block B and a rough horizontal tabletop.  Block B has a mass of 4.5 kg, and it is connected by a light inextensible string to a metal sphere A of mass 3.5 kg.  The string passes over a smooth light fixed pulley at the edge of the table so that A is hanging vertically downwards as shown in the diagram below:

The string between B and the table is horizontal, and the frictional resistance between B and the table is modelled as a constant force of magnitude F_f  N.

The system is released from rest with the string taut and with sphere A exactly 1 metre above the ground.

Given that sphere A strikes the ground 0.8 seconds after it is released, determine the value of F_f.

Luke Cloudwalker is a robotics engineer. Luke propels a robot along a straight path with initial speed  and uses a remote control to change its speed. Throughout the journey, the robot travels along the same straight path. The acceleration-time graph below shows the motion of the robot.