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

A car of mass 850 kg is moving up a straight road, inclined at an angle to the horizontal, along the line of greatest slope, where .  The engine of the car is working at a constant rate of 12.1 kW and the car is moving with a constant speed of  m s^-1.  The resistance to motion on the car from non-gravitational forces is  and acts parallel to the slope.

Justifying your answer, show that

The car later moves down the same hill along the line of greatest slope. It travels at the same speed as it did when it travelled up the hill.  The resistance to motion on the car from non-gravitational forces has increased to and the engine is now working at a constant rate of kW.

Show that 

.

Given that   =11.4, find the values of  and .

The acceleration, , of a particle moving in a straight line at time  is given by  for  . Initially the velocity of the particle is .

Find the time(s) when the particle is instantaneously at rest.

Find the exact total distance travelled by the particle in the first 6 seconds of motion.

Show your method clearly.

Kelsie is playing squash. The squash ball, of mass 0.025 kg, is moving with velocity  m s^-1  when Kelsie strikes it with her squash racket.  Immediately after being struck, the ball has velocity m s^-1.

Find the magnitude of the impulse exerted by the racket on the ball.

Find the angle between the vector and the impulse exerted by the racket.  Give your answer to 1 decimal place.

A non-uniform rod , of mass  kg and length 1.5 m, is resting against a rough wall at the point and is held in limiting equilibrium by a light inextensible string attached to it at the point .  The other end of the string is attached to the wall at the point vertically above such that 

Given that the tension in the string is 17 N, find the distance from of the centre of mass of the rod, in terms of the mass, .

Given that the coefficient of friction between the wall and the rod at the point is 0.3, find the mass of the rod and the distance from  of the centre of mass of the rod.

Two smooth spheres with the same radii have masses and respectively. The spheres are moving in opposite directions along a straight line on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of is and the speed of is . The collision causes the directions of motion to be reversed for both and . The coefficient of restitution between  is .

By modelling the spheres as particles, show that the speed of immediately after the collision is 

Find the range of possible values of .

Given that the speed of immediately after the collision is , explain why there is no change in the total kinetic energy before and after the collision.

A rectangular lamina, with vertices , is made from a uniform material of length 16 cm and width 4 cm as shown in Figure 1 below. A fold is created by taking vertex to the opposite side of the rectangle such that the side is coincident with the side , creating a fifth vertex  as shown in Figure 2 below.

Figure 1

Figure 2

Find the position of the centre of mass of the folded lamina in Figure 2, giving your answer as distances from the sides and .

The folded lamina in Figure 2 is allowed to freely pivot around the point that is 1 cm vertically above point . When in equilibrium find the angle between the downward vertical and the side .

A golfer strikes a ball from ground level with velocity

Find the distance the golf ball will travel before first hitting the ground.

Show that by reducing the angle of the strike above the horizontal by  the golfer can achieve approximately 7 m more distance before the ball lands.

Give a reason why the golfer may not want to achieve a longer distance with their shot.

A particle’s velocity is modelled by the equation

where  is the time in seconds.

The particle’s initial position is (3 , 5), find the position vector of the particle,  m, at time  seconds.

Find the time at which the particle’s acceleration, is zero in the horizontal  direction.