Velocity, acceleration and motion graphs

Speed is a scalar (size only); velocity is a vector (speed in a given direction). Acceleration is the rate of change of velocity: a = (v − u) ÷ t, in m/s². A negative acceleration is a deceleration. For uniform acceleration, v² − u² = 2 a s, where s is the distance.

On a distance–time graph the gradient gives the speed. On a velocity–time graph the gradient gives the acceleration, and the area under the graph gives the distance travelled. An object falling freely near the Earth accelerates at about 9.8 m/s². As it speeds up, air resistance increases until it equals the weight; then the resultant force is zero and it falls at a steady terminal velocity.