Example 1: finding acceleration
A runner increases her velocity from 3 m/s to 7 m/s in 2 s. Calculate her acceleration.
- Change in velocity = 7 − 3 = 4 m/s.
- acceleration = change in velocity ÷ time = 4 m/s ÷ 2 s.
- acceleration = 2 m/s².
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IB DemystifiedMYP Sciences
Acceleration
Speed tells you how fast. Acceleration tells you how quickly that is changing: pulling away, braking, even turning a corner. One graph shows all of it, and hides the distance travelled in its area.
Recommended for MYP 3 · About 3 lessons · Criteria A, B, C and D
On this page
Learning objectives
By the end of this topic you should be able to:
- distinguish speed from velocity
- state what acceleration means and give its unit
- calculate acceleration, and rearrange the equation to find a velocity or a time
- find acceleration from the gradient of a velocity–time graph
- find distance travelled from the area under a velocity–time graph
- describe the motion of falling objects, with and without air resistance
Before you start
You will use these skills. If any feel shaky, review them first.
- speed = distance ÷ time, and distance–time graphs (see the Speed topic)
- the gradient of a straight line
- the area of a rectangle and a triangle
Key vocabulary
- Velocity
- Speed in a stated direction, in m/s.
- Acceleration
- The rate of change of velocity, in m/s² (metres per second per second).
- Deceleration
- Negative acceleration: the velocity is decreasing.
- Velocity–time graph
- A graph of velocity against time. Its gradient is the acceleration; the area under it is the distance travelled.
- Free fall
- Falling under gravity alone. Near Earth's surface, the acceleration is about 9.8 m/s², often rounded to 10 m/s².
- Air resistance
- A force from the air that opposes motion and grows as speed increases.
Understanding acceleration
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What is it?
Acceleration is how much the velocity changes each second. A car accelerating at 2 m/s² gains 2 m/s of velocity every second.
acceleration = change in velocity ÷ time taken
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Why does it happen?
An object accelerates when the forces on it are unbalanced: an engine pushing harder than friction, brakes acting against the motion, or gravity pulling a falling stone. Because velocity has a direction, changing direction is also acceleration, even at a steady speed.
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How do we know?
We measure velocity at two moments, with light gates, motion sensors or video, and divide the change by the time between them. Galileo slowed falling motion down by rolling balls down gentle ramps, and found that their speed increased steadily: the first evidence that falling objects accelerate uniformly.
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Why does it matter?
Braking distances, car safety features, rollercoaster design and rocket launches all depend on acceleration. Engineers limit the acceleration of trains and lifts so that passengers stay comfortable and safe.
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What does it connect to?
Acceleration leads directly to Newton's laws, where force = mass × acceleration, and to momentum and energy. In mathematics it connects to gradients and to areas under graphs.
Velocity–time graphs
A velocity–time graph looks like a distance–time graph, but it is read differently.
- A sloping straight line means constant acceleration. Its gradient is the acceleration: in stage A of Figure 1, 20 m/s ÷ 10 s = 2 m/s².
- A flat line means constant velocity (zero acceleration), not standing still. A flat line along the time axis at 0 m/s means stationary.
- A downward slope means deceleration.
- The area under the line is the distance travelled. Split it into rectangles and triangles.
Acceleration in the real world
Electric cars feel lively because their motors give a large acceleration from a standstill. Lift designers keep accelerations to around 1 m/s², so passengers barely notice. Traffic engineers use deceleration values to set the length of yellow lights and the spacing of warning signs before junctions.
Worked examples
Example 2: distance from a velocity–time graph
A skateboarder speeds up steadily from rest to 6 m/s in 4 s. How far does she travel in that time?
- Sketch the graph: a straight line from (0 s, 0 m/s) to (4 s, 6 m/s), making a triangle.
- distance = area of the triangle = ½ × base × height.
- distance = ½ × 4 s × 6 m/s = 12 m.
Check your understanding
Quick questions on the ideas above. Try each one before using a hint.
Practice questions
Investigation: how does a trolley speed up on a ramp?
Guided investigation · about 50 minutes · groups of three
- Research question
- How does the velocity of a trolley released from rest on a fixed ramp change with time over the first 2.5 s?
- Scientific background
- On a ramp, part of the trolley's weight acts down the slope. If this unbalanced force stays the same, the trolley should gain the same amount of velocity every second: a constant acceleration.
- Hypothesis
- The velocity will increase in direct proportion to time, because a constant unbalanced force down the ramp gives a constant acceleration.
- Independent variable
- Time since release: readings every 0.5 s from 0 to 2.5 s.
- Dependent variable
- Velocity of the trolley, from a motion sensor or light gates.
- Control variables
- Same trolley and same ramp angle for every run, because either would change the force down the slope.
- Trolley released from rest from the same point, never pushed.
- Sensor fixed in the same position at the top of the ramp.
- Apparatus
- Ramp at least 2 m long, blocks to raise one end, trolley, motion sensor and data logger (or two light gates and a card), stopper at the bottom.
- Method
- Set up the ramp at a small, fixed angle with a stopper at the bottom.
- Place the motion sensor at the top, pointing down the ramp.
- Hold the trolley still in front of the sensor, start recording, then let go.
- Record the velocity every 0.5 s.
- Repeat three times and calculate a mean velocity at each time.
Safety. Fix a stopper at the bottom of the ramp and keep hands and feet out of the trolley's path. Check that the ramp is stable before each run.
Results from one group are used in the Criterion C questions below. Then evaluate: why is a motion sensor better than timing with a stopwatch for this investigation?
Criterion-linked questions
Criterion B: inquiring and designing
Criterion C: processing and evaluating
Criterion D: reflecting on the impacts of science
Challenge questions
Harder problems in unfamiliar contexts. Plan before you calculate.
Topic check
Five questions picked at random from the whole topic. Take a new set whenever you like.
Review your mistakes
Questions you got wrong on this device appear here so you can try them again. Answer one correctly and it leaves the list.
Your progress
Tracked separately for each skill, on this device only.
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