# Instantaneous Speed Formula

## 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 movement at any desired instant of time. 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 and x is the displacement.

Instantaneous speed formula 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
The instantaneous speed is given by

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

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

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

=(20(3)-5)

= 60-5

= 55m/s

Problem 2: A honey bee is alongside a path. Its position is provided by x = t2 + b. Compute its Instantaneous speed at time t = 2 s.

The position of honey bee is x = t2 + b

Its instantaneous speed is given by

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

$\dpi{120}&space;\large&space;S_{inst}=lim_{t>T}\frac{d(t^{2+b})}{dt}$

$\dpi{120}&space;\large&space;S_{inst}=lim_{t>T}(2t+0)$

= 2(2)

=4 m/s

The instaneous speed of honey bee is 4m/s