What you'll learn
This revision guide covers all aspects of Forces and Motion required for WJEC GCSE Physics. You'll master calculations involving speed, velocity and acceleration, understand Newton's laws of motion, analyse forces acting on objects, and apply these principles to real-world situations including vehicle safety. These concepts form the foundation for many other physics topics and appear regularly across all exam papers.
Key terms and definitions
Speed — the distance travelled per unit time, measured in metres per second (m/s) or kilometres per hour (km/h); a scalar quantity with magnitude only.
Velocity — the displacement per unit time in a specified direction, measured in m/s; a vector quantity with both magnitude and direction.
Acceleration — the rate of change of velocity, measured in metres per second squared (m/s²); can be positive (speeding up) or negative (deceleration/slowing down).
Resultant force — the single force that has the same effect as all the individual forces acting on an object combined together.
Inertia — the tendency of an object to remain at rest or continue moving at constant velocity unless acted upon by a resultant force.
Momentum — the product of an object's mass and velocity (p = mv), measured in kilogram metres per second (kg m/s); a vector quantity.
Thinking distance — the distance a vehicle travels during the driver's reaction time before the brakes are applied.
Braking distance — the distance a vehicle travels from when the brakes are applied until it comes to a complete stop.
Core concepts
Speed, velocity and distance-time graphs
Speed describes how fast an object moves without reference to direction. The equation linking distance, speed and time is:
speed = distance ÷ time
or v = s/t
When rearranged:
- distance = speed × time
- time = distance ÷ speed
Average speed considers the total distance covered over the total time taken. Instantaneous speed is the speed at any particular moment.
Velocity differs from speed because it includes direction. An object moving in a circle at constant speed is constantly changing velocity because its direction changes continuously.
Distance-time graphs show how far an object has travelled over time:
- Gradient (steepness) represents speed
- Horizontal line indicates the object is stationary
- Straight diagonal line shows constant speed
- Curved line indicates changing speed (acceleration or deceleration)
To calculate speed from a distance-time graph, find the gradient using: speed = change in distance ÷ change in time.
Acceleration and velocity-time graphs
Acceleration measures how quickly velocity changes. The equation is:
acceleration = change in velocity ÷ time taken
or a = (v - u)/t
where:
- a = acceleration (m/s²)
- v = final velocity (m/s)
- u = initial velocity (m/s)
- t = time (s)
A rearranged version gives: v = u + at
Deceleration is negative acceleration (slowing down). For example, a car reducing speed from 20 m/s to 10 m/s experiences negative acceleration.
Velocity-time graphs illustrate how velocity changes over time:
- Gradient represents acceleration
- Horizontal line shows constant velocity (zero acceleration)
- Upward slope indicates positive acceleration
- Downward slope shows deceleration
- Area under the graph equals distance travelled
To find distance from a velocity-time graph, calculate the area beneath the line. For rectangles use area = base × height; for triangles use area = ½ × base × height.
Newton's laws of motion
Newton's First Law states that an object remains at rest or continues moving at constant velocity unless acted upon by a resultant force. This is the principle of inertia.
Examples:
- A passenger lurches forward when a bus brakes suddenly (their body continues at constant velocity)
- A book rests on a table until someone pushes it
- A spacecraft in deep space continues moving without engines
Newton's Second Law relates force, mass and acceleration:
force = mass × acceleration
or F = ma
where:
- F = resultant force (N, newtons)
- m = mass (kg)
- a = acceleration (m/s²)
One newton is the force needed to accelerate 1 kg at 1 m/s². The larger the mass, the greater the force needed to produce a given acceleration. Doubling the force doubles the acceleration (if mass stays constant).
Newton's Third Law states that when object A exerts a force on object B, object B exerts an equal and opposite force on object A. These forces:
- Are equal in magnitude
- Act in opposite directions
- Act on different objects
- Are the same type of force
Examples:
- A swimmer pushes water backwards; water pushes the swimmer forwards
- Earth pulls you down with gravity; you pull Earth up with equal force
- A rocket expels hot gases downwards; gases push the rocket upwards
Momentum and collisions
Momentum (p) is defined as:
momentum = mass × velocity
or p = mv
Momentum is measured in kg m/s and is a vector quantity. A heavy lorry travelling slowly can have the same momentum as a light car travelling fast.
Conservation of momentum states that in a closed system, total momentum before a collision equals total momentum after, provided no external forces act:
total momentum before = total momentum after
or m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
This applies to:
- Collisions between vehicles
- Explosions where objects fly apart
- Interactions in snooker/pool
Force and momentum are linked. A force causes the rate of change of momentum:
force = change in momentum ÷ time
or F = (mv - mu)/t
This explains why safety features that increase collision time (crumple zones, airbags, seat belts) reduce the force experienced by passengers.
Forces and terminal velocity
Multiple forces typically act on moving objects. When forces are balanced (resultant force = 0), the object moves at constant velocity or remains stationary. When forces are unbalanced (resultant force ≠ 0), the object accelerates in the direction of the resultant force.
For objects falling through fluids (air or water):
- Weight acts downwards (W = mg)
- Drag (air resistance or water resistance) acts upwards, opposing motion
As an object accelerates downwards:
- Initially, weight exceeds drag, so resultant force is downwards causing acceleration
- As speed increases, drag increases (drag depends on speed)
- Eventually drag equals weight, so resultant force becomes zero
- Object continues at constant maximum velocity called terminal velocity
Skydivers demonstrate this:
- Fall from plane accelerating downwards (weight > drag)
- Reach terminal velocity around 50-60 m/s (weight = drag)
- Open parachute, dramatically increasing drag (drag > weight)
- Decelerate until new, lower terminal velocity is reached
- Land safely at this reduced speed
Stopping distances and vehicle safety
Total stopping distance = thinking distance + braking distance
Thinking distance depends on:
- Reaction time (typically 0.5-1.0 seconds)
- Initial speed of vehicle (higher speed = greater thinking distance)
- Driver alertness (tiredness, alcohol, drugs, distractions increase reaction time)
At constant reaction time, thinking distance is directly proportional to speed. Double the speed doubles the thinking distance.
Braking distance depends on:
- Initial speed (relationship is not linear; doubling speed quadruples braking distance)
- Road conditions (wet, icy roads reduce friction)
- Vehicle condition (worn brakes or tyres increase braking distance)
- Mass of vehicle (heavier vehicles take longer to stop)
Typical stopping distances at different speeds:
- 30 mph (13 m/s): 9m thinking + 14m braking = 23m total
- 60 mph (27 m/s): 18m thinking + 55m braking = 73m total
- 70 mph (31 m/s): 21m thinking + 75m braking = 96m total
Safety features reduce injury by:
- Increasing collision time (crumple zones, airbags) to reduce force on passengers
- Absorbing energy (crumple zones convert kinetic energy to deformation)
- Preventing impact with hard surfaces (airbags, padding)
- Spreading force over larger area (seat belts)
- Preventing ejection from vehicle (seat belts)
Worked examples
Example 1: Speed calculation
A cyclist travels 180 metres in 15 seconds. Calculate the cyclist's average speed.
Solution:
- speed = distance ÷ time
- speed = 180 ÷ 15
- speed = 12 m/s
[2 marks: 1 mark for correct substitution into equation, 1 mark for correct answer with unit]
Example 2: Acceleration calculation
A car accelerates from rest to 25 m/s in 8.0 seconds. Calculate the acceleration of the car.
Solution:
- acceleration = change in velocity ÷ time taken
- a = (v - u)/t
- a = (25 - 0)/8.0
- a = 3.125 m/s²
- a = 3.1 m/s² (to 2 s.f.)
[3 marks: 1 mark for correct formula, 1 mark for correct substitution, 1 mark for answer with unit]
Example 3: Force and acceleration
A resultant force of 600 N acts on a car of mass 1200 kg. Calculate the acceleration produced.
Solution:
- F = ma, so a = F/m
- a = 600/1200
- a = 0.5 m/s²
[3 marks: 1 mark for rearranging formula correctly, 1 mark for substitution, 1 mark for answer with unit]
Example 4: Conservation of momentum
A 1000 kg car travelling at 15 m/s collides with a stationary 800 kg car. After collision, they move together. Calculate their velocity immediately after collision.
Solution:
- Total momentum before = total momentum after
- m₁u₁ + m₂u₂ = (m₁ + m₂)v
- (1000 × 15) + (800 × 0) = (1000 + 800)v
- 15000 = 1800v
- v = 15000/1800
- v = 8.3 m/s (to 2 s.f.)
[4 marks: 1 mark for conservation principle, 1 mark for correct equation setup, 1 mark for working, 1 mark for answer with unit]
Common mistakes and how to avoid them
Confusing speed and velocity. Remember: velocity includes direction; speed does not. An object moving in a circle at constant speed has changing velocity.
Mixing up distance-time and velocity-time graphs. On distance-time graphs, gradient = speed and the line never goes down. On velocity-time graphs, gradient = acceleration and area under graph = distance.
Forgetting units or using incorrect units. Always include units in final answers. Standard SI units: m/s for speed/velocity, m/s² for acceleration, N for force, kg m/s for momentum.
Applying Newton's Third Law incorrectly. The equal and opposite forces act on different objects, not the same object. They cannot cancel each other out because they act on different things.
Assuming braking distance is directly proportional to speed. Doubling speed quadruples braking distance, not doubles it. This is because kinetic energy (which must be dissipated) is proportional to speed².
Missing the formula triangle method. While formula triangles aren't always shown in mark schemes, they help rearrange equations correctly. Practice rearranging v = s/t, a = (v-u)/t, and F = ma algebraically.
Exam technique for "Forces and Motion"
Command words matter. "Calculate" requires working and a numerical answer with units. "Describe" needs a sequential account. "Explain" requires reasons or mechanisms using physics principles.
Show all working for calculations. Even if your final answer is wrong, you can earn method marks for correct formula, substitution, or rearrangement. Write the formula first, then substitute values, then calculate.
Read velocity-time graphs carefully. When asked for distance, calculate the area under the graph by dividing it into rectangles and triangles. For acceleration, find the gradient. Students often confuse these.
Use data from the question. Marks are often awarded for correctly extracting and using given values. If a question provides information, you almost certainly need to use it.
Quick revision summary
Forces and Motion combines calculations and conceptual understanding. Master the core equations: v = s/t for speed, a = (v-u)/t for acceleration, F = ma for force, and p = mv for momentum. Understand that distance-time graph gradients show speed while velocity-time graph gradients show acceleration and areas show distance. Newton's laws explain why objects move or stay still. Momentum is conserved in collisions. Terminal velocity occurs when weight equals drag. Stopping distance combines thinking and braking distances, both affected by different factors. Safety features increase collision time to reduce forces on passengers.