Forces and motion · GCSE Physics
Motion
Speed and velocity, distance–time and velocity–time graphs, acceleration, F = ma, and kinetic and gravitational energy in moving systems.
The slope of a distance–time graph is speed. The slope of a velocity–time graph is acceleration. The area under a velocity–time graph is displacement. Write that before you reach for a formula.
The important bits
What you need to know
- 1
Speed is scalar; velocity is speed in a given direction. Average speed = distance / time. A typical walking, running and cycling speed, and the 30 mph urban speed limit in m/s, are worth knowing for sense checks.
- 2
Acceleration a = Δv / t. It is a vector. Slowing down is negative acceleration if the chosen direction is forwards. Units: m/s².
- 3
Distance–time: straight line up means constant speed; horizontal means stationary; a curve getting steeper means speeding up. Gradient = speed.
- 4
Velocity–time: straight line up means constant acceleration; horizontal means constant velocity; area under the line = distance travelled. Gradient = acceleration.
- 5
v² − u² = 2as is the motion equation used when time is not given. F = ma links a resultant force to that acceleration. Both need SI units.
- 6
Kinetic energy E = ½mv² and gravitational potential energy E = mgh often sit in the same question as motion: a falling object transfers g.p.e. to kinetic if dissipative forces are ignored.
- 7
On Higher tier, momentum p = mv is conserved in a closed system. A force causes a change in momentum: F = Δp / t. Airbags and crumple zones increase t, so F falls.
Go deeper
Graphs before algebra
If the paper gives a graph, they want a gradient or an area, not a memorised story. On a distance–time graph, pick two points on a straight section, rise over run, include units. A closed loop back to the start on a displacement graph would mean you had come home; GCSE usually plots distance, which only rises or stays. On a velocity–time graph, a line below the time axis is motion the other way. The area between the line and the axis is still distance travelled for that interval; subtract areas if you need displacement. Students count squares and then forget the value of each square. Write the scale first: each square is, say, 2 m/s by 1 s, so 2 m.
Go deeper
Falling and braking are energy as well as motion
A ball dropped from rest: mgh at the top becomes ½mv² at the bottom if air resistance is ignored, so v = √(2gh). That matches v² = u² + 2as with u = 0 and a = g. If a question mentions heat and sound, some g.p.e. is dissipated and the speed is less. A car braking is the reverse: ½mv² is transferred by the work the brakes do. That is why braking distance grows with v². When F = ma is used, F is resultant: weight minus drag for a falling skydiver who has not reached terminal velocity. At terminal velocity, a = 0, so resultant F = 0, even though speed is large.
See the idea in action
A cyclist accelerates from 4.0 m/s to 10.0 m/s in 6.0 s. a = (10 − 4) / 6 = 1.0 m/s². If the combined mass is 80 kg, resultant force F = ma = 80 × 1.0 = 80 N forwards. On a velocity–time graph that is a straight line from 4 to 10 in 6 s. Distance = area of the trapezium = ½ × (4 + 10) × 6 = 42 m. Checking with v² − u² = 2as: 100 − 16 = 2 × 1.0 × s, so s = 42 m. The two methods agree.
Exam technique
Turn knowledge into marks
State which graph you are reading: gradient of s–t is speed, gradient of v–t is acceleration, area of v–t is distance. Keep u, v, a, s, t in a list before you choose an equation. For F = ma, write “resultant force”. Convert km/h to m/s by dividing by 3.6.
Common mistakes
Do not give these marks away
- 01
Reading a distance–time slope as acceleration, or forgetting that area under a v–t graph is distance.
- 02
Using F = ma with one force when two forces act in opposite directions.
- 03
Leaving speed in kilometres per hour when the rest of the data are in metres and seconds.
What does the area under a velocity–time graph represent?
AAcceleration
BForce
CDistance travelled
DMass
Show the answer
Distance travelled. Velocity × time is distance when velocity is constant, and the area under a varying v–t graph generalises that product. Gradient would be acceleration.
Quick questions
If this is the bit you searched
How do you find acceleration from a velocity–time graph?
Calculate the gradient: change in velocity divided by change in time. A horizontal line means zero acceleration (constant velocity).
What is the difference between speed and velocity?
Speed is how fast something moves. Velocity is speed in a stated direction, so it is a vector. Circular motion at constant speed still has changing velocity.