Class 11 Physics Formula Sheet 2026-27

2.2 INSTANTANEOUS VELOCITY AND SPEED

Knowing the average velocity of a body over an interval tells us its overall rate of displacement during that interval, but it gives no information about how fast the body was moving at any particular moment within it. A car that covers 60 km in one hour may have been stationary at a signal for some minutes and travelling at 90 km/h at other times. To describe motion at a given moment we need the idea of instantaneous velocity.

Suppose the interval over which the average velocity is calculated is made shorter and shorter around the instant t. The average velocity then approaches a definite value, and this limiting value is taken as the velocity at the instant t. Using the notation of calculus,

that is, the velocity at an instant is the derivative of position with respect to time. Graphically, it is the slope of the tangent to the position–time curve at that instant. The magnitude of the instantaneous velocity is the instantaneous speed.

When the velocity itself changes with time, the body is said to be accelerated. The rate of change of velocity with time is called acceleration, and its value at an instant is obtained in the same way, as the limit a = dv/dt.