A.1 · 6 · A.1 Kinematics · distance, displacement, speed, velocity, acceleration
Terms to describe motion
Position, distance, displacement, speed, velocity and acceleration: which are vectors, and why the difference matters.
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Hook
You walk 3 m east and then 4 m north. How far did you walk? How far are you from where you started? Those are two different questions with two different answers.
1 · Position
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Which of these is a vector?
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You run once around a 400 m track and finish where you started. Your displacement is…
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A car speeds up from 4 m s⁻¹ to 16 m s⁻¹ in 3 s. Its acceleration is…
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A ball at 3 m s⁻¹ accelerates at 2 m s⁻² for 5 s. Its final velocity is…
Apply
A drone flies 6 m east and then 8 m north in 5 s. Find its distance, its displacement, its average speed and the size of its average velocity.
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Remember earlier lessons
From lesson A.1 · 5
A vector splits into two components at…
From lesson A.1 · 4
Uniform motion has acceleration…
Summary card
Key points
- • Distance (scalar) is the length of the path; displacement (vector) is the straight line from start to end.
- • Speed = distance / time. Velocity = displacement / time.
- • Acceleration is the rate of change of velocity, a = (v − u) / t, so v = u + at.
Formulas
- Δx = vt
- a = (v − u) / t
- v = u + at
Key terms
- Displacement :
- shortest route from start to end, a vector
- Acceleration :
- rate of change of velocity, in m s⁻²
Common errors
- • Calling Δx / t the average speed.
- • Adding distances when the question asks for displacement.
- • Writing the unit of acceleration as m s⁻¹.
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