# Instantaneous Speed Formula

The speedometer givesĀ the record of speed for each instantĀ ofĀ time. This givesĀ the illustration of instantaneousĀ speed. Instantaneous speedĀ is the speed of a particle in the movement at any desired instant of time.

## Formula of Instantaneous Speed

Its formula is articulated as

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

Where,

• t is the time taken
• x is the displacement

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

### Instantaneous Speed Solved Examples

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

ProblemĀ 1:Ā A particle experiences the displacement given by the function x(t) = 10 t2Ā – 5t + 1. Compute its instantaneous speed at time t = 3s.

Given :

The function is given by x(t) = 10 t2Ā – 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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