Elective Mathematics

1A 5 kg mass is pulled up a smooth 30° incline by a force parallel to it. The force needed for constant velocity is (g = 10 m/s²)

2A 4 kg mass on a smooth plane inclined at 30° is released. Its acceleration down the plane is (g = 10 m/s²)

3Two forces of 3 N and 4 N act at right angles. Their resultant is

4A particle moves so that s = t³ − 6t² + 9t. It is momentarily at rest when t =

5Two forces of 3 N and 4 N act at right angles on a particle. Find the magnitude of their resultant.

6A ball is projected horizontally at 10 m/s from a height of 20 m (g = 10 m/s²). How far from the foot of the cliff does it land?

7A body of mass 4 kg moves with velocity (3i + 4j) m/s. What is its kinetic energy?

8A car accelerates from 10 m/s to 30 m/s over 200 m. Its acceleration is

9The impulse of a force of 10 N acting for 0.5 s is

10A particle moves so that its displacement is s = t³ − 3t metres. Find its velocity at t = 2 s.