Displacement, velocity, acceleration and motion graphs

Physics · Motion and force. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Distance is the length of the path travelled. Displacement is the straight-line change of position from start to finish, with a direction. Speed uses distance; velocity uses displacement. Average velocity covers a whole time interval, while instantaneous velocity is the value at one moment, found as the interval is made very small.

Acceleration is the rate of change of velocity. On a velocity-time graph the gradient gives the acceleration and the area under the graph gives the distance covered. On a displacement-time graph the gradient gives the velocity.

When the acceleration is uniform, three equations link the five quantities. A body in free fall has a = g = 9.8 m s−2 downwards.

Rules to remember

Common mistake

Students mix up the signs in vertical motion. Choose one direction as positive at the start and give every velocity, displacement and acceleration a sign that fits it.

Worked example

A train moving at 15 m s−1 accelerates uniformly at 0.50 m s−2 over a distance of 400 m. Find its final velocity and the time taken.

  1. 2aS = vf2 − vi2, so vf2 = 152 + 2 × 0.50 × 400 = 225 + 400 = 625.
  2. vf = √625 = 25 m s−1.
  3. t = (vf − vi) ÷ a = (25 − 15) ÷ 0.50 = 20 s.

Answer: 25 m s−1, reached after 20 s

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