Instantaneous Speed Formula

The speedometer gives the record of speed for each instant of time. This gives the illustration of instantaneous speed. Instantaneous speed is the speed of a particle in the movement at any desired instant of time.

Formula of Instantaneous Speed

Its formula is articulated as

\(\begin{array}{l}S_{\text{inst}}=\lim_{t\to T} \frac{dx}{dt}\end{array} \)


  • t is the time taken
  • x is the displacement

It is made use of to calculate the rate of change of displacement for any given instant of time. It is articulated in meter per second (m/s).

Instantaneous Speed Solved Examples

Below are some problems based on instantaneous speed which may be helpful for you.

Problem 1: A particle experiences the displacement given by the function x(t) = 10 t2 – 5t + 1. Compute its instantaneous speed at time t = 3s.


Given :

The function is given by x(t) = 10 t2 – 5t + 1

t = 3s

The instantaneous speed is given by

\(\begin{array}{l}S_{\text{inst}}=\lim_{t\to T} \frac{dx}{dt}\end{array} \)
\(\begin{array}{l}=\lim_{t\to 3}\frac{d(10t^2 – 5t + 1)}{dt}\end{array} \)
\(\begin{array}{l}=\lim_{t\to 3} (20t – 5)\end{array} \)

Sinst =(20(3)-5)

Sinst = 60-5

Sinst = 55m/s

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