Kinematics

Physics · Space, time and motion. 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

Displacement is the straight-line distance from start to finish, with a direction. Distance is the length of the path travelled. Velocity is the rate of change of displacement, so it is a vector; speed is a scalar. An average value covers a whole journey. An instantaneous value belongs to one moment.

When the acceleration is constant, the four equations of motion link s, u, v, a and t. On a graph, a gradient gives a rate and an area gives a total.

A projectile has two independent motions: a constant horizontal velocity and a vertical acceleration g downwards. Time links the two. Air resistance reduces the range and the height. A falling object reaches terminal speed when the drag equals its weight.

Rules to remember

Common mistake

Students say that a projectile has zero velocity or zero acceleration at the top of its path. Only the vertical component of velocity is zero there; the acceleration is still 9.8 m s−2 downwards.

Worked example

A ball is thrown horizontally at 6.0 m s−1 from a window and hits the ground 1.5 s later. Air resistance is negligible and g = 9.8 m s−2. What is its speed as it hits the ground?

  1. The horizontal velocity does not change: 6.0 m s−1.
  2. Vertical velocity: v = u + at = 0 + 9.8 × 1.5 = 14.7 m s−1.
  3. Combine the components: speed = √(6.02 + 14.72) = √(36 + 216) = √252.

Answer: About 16 m s−1.

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