Motion and force

NUST NET Physics · Physics · Mechanics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

For motion in a straight line with constant acceleration, four equations link u, v, a, s and t. Pick the one that leaves out the quantity you do not know or need. On a velocity-time graph the gradient is the acceleration and the area underneath is the displacement.

Newton's second law says force is the rate of change of momentum, so a force acting for a time gives an impulse equal to the change in momentum. Total momentum is conserved in every collision; kinetic energy is conserved only in an elastic one.

A projectile is two motions at once: constant velocity horizontally (u cos θ) and free fall vertically (starting at u sin θ).

Rules to remember

Common mistake

Saying a projectile has zero velocity at its highest point. Only the vertical part is zero there; the speed is still u cos θ and the acceleration is still g downwards.

Worked example

A stone is thrown horizontally at 15 m s−1 from the top of a cliff 20 m high. Taking g = 10 m s−2, how far from the foot of the cliff does it land?

  1. Vertically it starts from rest: h = ½gt2, so t2 = 2h/g = (2 × 20)/10 = 4 and t = 2 s.
  2. Horizontally the velocity stays at 15 m s−1.
  3. Distance = 15 × 2 = 30 m.

Answer: 30 m

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