Motion and Forces: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 3 · 9478 Topic 3 · Read time: ~11 minutes
These notes come from TGC Academy's A Level H2 Physics tuition in Singapore. Checking your rank points? Try our free RP calculator.
Key Formulas
Describing motion with graphs
Distance and speed are scalars. Displacement, velocity and acceleration are vectors, so direction and sign matter.
Gradient of a displacement-time graph = velocity. Gradient of a velocity-time graph = acceleration. Area under a velocity-time graph = displacement.
For non-uniform acceleration the graph curves: use the gradient of the tangent at a point, and estimate areas by counting squares or splitting into shapes.
Trap: Constant acceleration is a straight sloped line on a v-t graph, which is a horizontal line on the a-t graph. Students often sketch the a-t graph with the same shape as the v-t graph.
Uniformly accelerated motion
The four equations come straight from the definitions a = (v − u)/t and displacement = area under the v-t graph. They apply only while acceleration is constant; otherwise split the motion into stages.
Free fall without air resistance near the Earth: a = g = 9.81 m s⁻² downwards, for the whole flight, going up and coming down.
Pick a positive direction at the start and apply it to every vector. Pick the equation that leaves out the quantity you don't know and don't need.
Trick: A ball thrown upwards has zero velocity at the top but its acceleration is still g downwards. 'Momentarily at rest' never means 'zero acceleration'.
Mass, momentum and Newton's laws
Mass is the property of a body that resists change in its motion (inertia). Linear momentum p = mv.
1st law: a body at rest stays at rest, and a body in motion keeps moving at constant velocity, unless acted on by a resultant external force.
2nd law: the rate of change of momentum of a body is proportional to the resultant force acting on it, and in the same direction. For constant mass this gives F = ma.
3rd law: the force exerted by one body on a second body is equal in magnitude and opposite in direction to the force simultaneously exerted by the second body on the first.
Trap: Learn the 9478 wording of each law. The second law is about rate of change of momentum; writing only 'F = ma' as a definition usually loses the definition mark.
Worked Example
A ball of mass 0.20 kg is thrown vertically upwards at 15 m s⁻¹ from the edge of a cliff, and lands in the sea 25 m below the launch point. Air resistance is negligible. Take g = 9.81 m s⁻².
(a) Calculate the maximum height reached above the launch point. [2]
At the top, v = 0. Taking up as positive: v² = u² + 2as
0 = 15² + 2(−9.81)s
s = 225 ÷ 19.62 = 11.5 m
(b) Calculate the speed of the ball as it hits the sea. [2]
Displacement s = −25 m
v² = 15² + 2(−9.81)(−25) = 225 + 490.5 = 715.5
Speed = 26.7 m s⁻¹
(c) Calculate the change in momentum of the ball between leaving the hand and hitting the sea. [2]
Initial momentum = 0.20 × 15 = +3.0 kg m s⁻¹
Final momentum = 0.20 × (−26.7) = −5.35 kg m s⁻¹
Change = −5.35 − 3.0 = −8.35 kg m s⁻¹, i.e. 8.35 kg m s⁻¹ downwards
Why this question is a good test of the topic: the whole flight is one stage of constant acceleration, so one sign convention carries through. Part (c) catches students who subtract speeds instead of signed velocities.
Frequently Asked Questions
What is the difference between distance and displacement?
Distance is the total path length, a scalar. Displacement is the straight-line change in position with a direction, a vector.
When can I use the SUVAT equations?
Only during a stage where acceleration is constant. For changing acceleration, split the motion into stages or use a graph.
How does 9478 state Newton's second law?
The rate of change of momentum of a body is proportional to the resultant force acting on it and is in the same direction as the resultant force.
What is inertia?
The property of a body that resists change in its motion. Mass is the measure of inertia.
What does the area under a velocity-time graph give?
Displacement. Areas below the time axis count as negative displacement.
SUVAT and Newton's laws questions taking too long?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.