Average and Instantaneous Speed

Average speed = total distance ÷ total time takeninstantaneous speed is the speed at a particular time and is the gradient of the tangent of a distance-time graph at a particular time t.average speed = total distance ÷ total timeAverage speed ignores any changes in speed during a journey. A train that covers 180 km in 2.0 hours has an average speed of 90 km h^-1, even though it stopped at stations and at times travelled faster than this.Worked example: a cyclist rides 1200 m in 150 s, rests for 50 s, then rides 800 m in 100 s.average speed = (1200 + 800) ÷ (150 + 50 + 100) = 2000 ÷ 300 = 6.7 m s^-1The rest time counts, because it is part of the total time.Instantaneous speed is what a speedometer shows. On a curved distance-time graph, draw a tangent to the curve at time t, make a large triangle on it, and divide its rise (distance) by its run (time). The steeper the tangent, the greater the instantaneous speed.If the speed is constant, the instantaneous speed equals the average speed at every moment. In the lab, instantaneous speed can be measured with a light gate: speed = length of the card ÷ time the card blocks the beam.