ZIMSEC A Level · Physics · Form 5
Equations of uniformly accelerated motion
v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t.
Projectiles
Treat horizontal (constant velocity) and vertical (acceleration g = 9.81 m s⁻² downwards) motion separately.
Worked example: A ball is thrown horizontally at 15 m s⁻¹ from a cliff 20 m high. Find the time of flight and horizontal distance.
Vertical: 20 = ½ × 9.81 × t² → t = 2.02 s
Horizontal: x = 15 × 2.02 = 30.3 m
Newton's laws and momentum
- F = ma, or more generally F = Δp/Δt (rate of change of momentum).
- Momentum p = mv is conserved in all collisions when no external force acts.
- Elastic collisions also conserve kinetic energy; in inelastic collisions KE is lost. For elastic collisions, relative speed of approach = relative speed of separation.
Worked example: A 2.0 kg trolley at 3.0 m s⁻¹ collides and sticks to a 1.0 kg stationary trolley. Find their common velocity.
2.0 × 3.0 = 3.0 × v → v = 2.0 m s⁻¹
Terminal velocity and drag
Drag increases with speed; terminal velocity is reached when drag + upthrust = weight.
Exam tip: Choose a positive direction and stick to it – most momentum errors are sign errors.
Check yourself
- A car accelerates from 5 m s⁻¹ to 25 m s⁻¹ over 100 m. Find its acceleration.
- A 0.15 kg ball hits a wall at 20 m s⁻¹ and rebounds at 15 m s⁻¹. Find the change in momentum.
- State the principle of conservation of momentum.
Show answers
- a = (625 − 25)/200 = 3.0 m s⁻²
- 0.15 × (15 − (−20)) = 5.25 kg m s⁻¹ (away from the wall)
- The total momentum of a system remains constant if no resultant external force acts on it.
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