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# Mathematics Past Papers

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Q 1: If a force of 1000 N is applied over a vehicle of 500 kg, then in how much time the speed of the vehicle will increase from 2 m/s to 10 m/s?

Q 2: An object gets the velocity of 10 m/s after applying a force of 500N for 5 second. If the mass of the object is equal to 1000 kg, what was its velocity before applying the force?

Q 3: A car is travelling at 20 m/s along a road. A child runs out into the road 50 m ahead and the car driver steps on the brake pedal. What must the car's deceleration be if the car is to stop just before it reaches the child?

Q 4: Find the resultant force that would give a body of mass 3kg an acceleration of 2ms–2 . Find the mass of the body?

Q 5: A 77-kg person is parachuting and experiencing a downward acceleration of 2.5 m/s2 shortly after opening the parachute. The mass of the parachute is 5.2 kg.

(a) Find the upward force exerted on the parachute by the air.

(b) Calculate the downward force exerted by the person on the parachute.

Q 6: The hot air balloon shown in the diagram, rises from the ground with uniform acceleration. After 10s the balloon has attained a height of 25m. If the total mass of the balloon and basket is 250kg, find the magnitude of the lifting force F.

Q 7: A child's toy consists of three cars that are pulled in tandem on small frictionless rollers as shown in below figure. The cars have masses m1 = 3.1 kg, m2 = 2.4kg, and m3 = 1.2 kg. If they are pulled to the right with a horizontal force P = 6.5 N, find

(a) the acceleration of the system,

(b) the force exerted by the second car on the third car, and

(c) the force exerted by the first car on the second car.

Q 8: Two blocks are in contact on a frictionless table. A horizontal force is applied to one block, as shown in the below figure.

(a) If m1 = 2.3 kg, m2 = 1.2 kg, and F = 3.2 N, find the force of contact between the two blocks.

(b) Show that If the same force F is applied to m2 rather than to m1, the force of contact between the blocks is 2.1 N, which is not the same value derived in (a). Explain.

Q 9: Particles of mass 4kg and 2kg are connected by a light string passing over a smooth fixed pulley. The particles hang freely and are released from rest. Find the acceleration of the two particles and the tension in the string. Let the acceleration be a and the tension in the string be T.

Q 10: Each of the following diagrams shows two freely hanging masses connected by a light inextensible string passing over a smooth fixed pulley. For each system find:

(a) The acceleration of the masses.

(b) The magnitude of the tension T1

(c) The magnitude of the tension T2

Q 1: A bullet of mass 15 g has a speed of 400 m/s. What is its kinetic energy ? The bullet strikes a thick target and is brought to rest in 2 cm, calculate the average net force acting on the bullet. What happens to kinetic energy originally in the bullet?

Q 2: During the Powerhouse lab, Sara runs up the stairs, elevating his 102 kg body a vertical distance of 2.29 meters in a time of 1.32 seconds at a constant speed.

(a) Determine the work done by Sara in climbing the stair case.

(b) Determine the power generated by Sara.

Q 3: A rough surface is inclined at tan-1 7/24 to the horizontal. A body of mass 5kg lies on the surface and is pulled at a uniform speed a distance of 100cm up the surface by a force acting along a line of greatest slope. The coefficient of friction between the body and the surface is 5/12. Find:

(a) The work done against gravity

(b) The work done against friction

Q 4: A pendulum of length 1m and with a bob pf mass 1 kg swings in a vertical plane. Find the work done by weight of the bob when it moves from position A to B

Q 5: A car of mass 800kg pulls a trailer of mass 300kg. The force produced by the engine is 4000N. The resistances acting on the car and trailer are 500 N and 200 N respectively. Calculate:

(a) The acceleration of the car and trailer.

(b) The tension in the towbar

Q 6: A small object of mass m = 234 g slides along a track with elevated ends and a central flat part, as shown in below figure. The flat part has a length L = 2.16 m. The curved portions the tracks are frictionless; but in traversing the flat part, the object loses 688 mJ of mechanical energy, due to friction. The object is released at point A, which is a height h = 1.05 m above the flat part of the track. Where does the object finally come to rest?

Q 7: A boy whose mass is 60 kg, has a sledge of ass 8 kg. he pulls the sledge 36m up a slope inclined at 30 degree to the horizontal.

(a) Find the amount of work that the boy has to exert against gravity in order to pull the sledge up.

(b) The boy then sits on the sledge and slides back to the foot of the slope. Find the work done by gravity during the descent

Q 8: A small object of mass m = 234 g slides along a track with elevated ends and a central flat part, as shown in below figure. The flat part has a length L = 2.16 m. The curved portions the tracks are frictionless; but in traversing the flat part, the object loses 688 mJ of mechanical energy, due to friction. The object is released at point A, which is a height h = 1.05 m above the flat part of the track. Where does the object finally come to rest?

Q 9: A girl to swing across the stream of a rope, which is attached to an overhanging tree at point A. The bank on the opposite side of the stream is 1.6m higher than the bank of which she is standing. At what speed must she push off in order just to get there?

Q 10: A car of mass 900 kg has an engine with power output of 42 kW. It can achieve a maximum speed of 120 km/h along the level.

(a) What is the resistance to motion?

(b) If the maximum power and the resistance remained the same what would be the maximum speed the car could achieve up an incline of 1 in 40 along the slope?

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