# 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

$\dpi{120}&space;\large&space;S_{inst}=\lim_{lim_{t\rightarrow&space;T}}\frac{dx}{dt}$

Where,

• 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

$\dpi{120}&space;\large&space;S_{inst}=\lim_{lim_{t\rightarrow&space;T}}\frac{dx}{dt}$

$\dpi{120}&space;\large&space;lim_{t\rightarrow&space;3}\frac{d(10t^{2}-5t+1)}{dt}$

$\dpi{120}&space;\large&space;lim_{t\rightarrow&space;3}(20t-5)$

Sinst =(20(3)-5)

Sinst = 60-5

Sinst = 55m/s

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