Motion and Forces
Analyse motion using speed, velocity, and acceleration formulas. Interpret distance-time and velocity-time graphs. Apply Newton's three laws of motion.
Describing Motion
Motion is described using three key quantities. Understanding the difference between speed (scalar) and velocity (vector) is essential for physics.
s = d / t
Unit: m/s
Distance covered per unit time.
Scalar (magnitude only).
v = Δx / t
Unit: m/s
Displacement per unit time.
Vector (magnitude + direction).
a = Δv / t
Unit: m/s²
Rate of change of velocity.
Vector quantity.
Key difference: Speed tells you how fast something moves. Velocity tells you how fast AND in which direction. An object moving at 10 m/s north has a different velocity from one moving at 10 m/s south, even though their speeds are the same.
Motion Graphs
Distance-Time Graph
- Gradient = speed
- Straight line = constant speed
- Horizontal line = stationary (speed = 0)
- Steeper gradient = faster speed
- Curved line = changing speed (acceleration)
Velocity-Time Graph
- Gradient = acceleration
- Area under line = distance travelled
- Horizontal line = constant velocity (a = 0)
- Upward slope = acceleration
- Downward slope = deceleration
Newton's Three Laws of Motion
First Law — Inertia
“An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by an unbalanced force.”
Example: A soccer ball remains still on the ground until kicked. A passenger lurches forward when a bus brakes suddenly because their body tends to continue moving forward (inertia).
Second Law — F = ma
“The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.”
F = m × a
Force (N) = mass (kg) × acceleration (m/s²)
Example: Pushing a shopping trolley (small mass) requires less force than pushing a car (large mass) to achieve the same acceleration.
Third Law — Action-Reaction
“For every action, there is an equal and opposite reaction.”
Example: When you push against a wall, the wall pushes back on you with an equal force. A rocket propels exhaust gases downward (action), and the gases push the rocket upward (reaction).
Note: The action and reaction forces act on different objects — they do not cancel out.
Key Vocabulary
| Term | Definition |
|---|---|
| Displacement | The straight-line distance and direction from start to finish (vector quantity). |
| Acceleration | The rate of change of velocity, measured in m/s². |
| Net force | The overall force acting on an object (sum of all forces including direction). |
| Inertia | The tendency of an object to resist changes in its state of motion. |
| Newton (N) | The SI unit of force; 1 N = 1 kg × m/s². |
| Friction | A contact force that opposes the relative motion of two surfaces. |
Worked Examples
Calculate the acceleration of a car.
Question: A car accelerates from 10 m/s to 30 m/s in 5 seconds. Find its acceleration.
Formula: a = Δv / t = (vfinal − vinitial) / t
Substitution: a = (30 − 10) / 5 = 20 / 5
Answer: a = 4 m/s²
Calculate the force required to accelerate a trolley.
Question: A 25 kg trolley is pushed with a constant acceleration of 2 m/s². What is the net force?
Formula: F = m × a
Substitution: F = 25 × 2
Answer: F = 50 N
Interpreting a velocity-time graph.
Question: A velocity-time graph shows a straight line from (0, 0) to (8, 20). Calculate (a) the acceleration and (b) the distance travelled.
(a) Acceleration = gradient = rise/run = (20 − 0) / (8 − 0) = 2.5 m/s²
(b) Distance = area under the graph = area of triangle = ½ × base × height
Distance = ½ × 8 × 20 = 80 m
Knowledge Check
Select the correct answer for each question. Click “Check Answer” to see feedback.
Question 1
A cyclist travels 150 metres in 30 seconds. What is their average speed?
Question 2
On a distance-time graph, a horizontal line represents:
Question 3
A 60 kg skater pushes off a wall. Using Newton's Third Law, which statement is correct?
Question 4
What net force is needed to give a 1,200 kg car an acceleration of 3 m/s²?
Question 5
On a velocity-time graph, what does the area under the line represent?
Key Concepts Summary
- •Speed = d/t; velocity = displacement/time; acceleration = Δv/t.
- •Distance-time graphs: gradient = speed. Velocity-time graphs: gradient = acceleration, area = distance.
- •Newton's 1st Law: Objects resist changes in motion (inertia).
- •Newton's 2nd Law: F = ma — force equals mass times acceleration.
- •Newton's 3rd Law: Every action has an equal and opposite reaction.