Velocity from distance-time graph
When a body moves with uniform velocity it will travel equal distances in equal intervals of time, and so a graph of distance against time will be a straight line (Fig. 3.3 (a)). Now if we take any point A, on the graph and drop a perpendicular AB on
to the time axis, it is clear that AB represents the distance moved in the time interval represented by OB.
Fig. 3.3 (b) is a graph of distance against time for a body moving with a maria velocity. In order to find the velocity at any instant represented by point A 0 curve, let us imagine a very small right-angled triangle BCD to be drawn whose
hypotenuse BD is so short that it effectively coincides with the curve in the immediate neighbourhood of A. In other words, we are considering a portion of the curve which is sufficiently short to be regarded as sensibly straight.
It would, of course, be of little use attempting to get accurate results from measurements made on so small a triangle. Instead we may find the velocity from a much larger similar triangle obtained by drawing a tangent EG to the curve at A, and measuring its gradient.
time interval EF velocity at A.