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Instantaneous Velocity Formula

Let us Consider a cyclist riding, his velocities varies continuously depending on time, distance etc. At any particular instant if we want to find his velocity its nothing but instantaneous velocity.

Formula for Instantaneous Velocity
Instantaneous Velocity Formula is used to determine the instantaneous velocity of the given body at any particular instant. It is given as:

Where x is the given function with respect to time t. The Instantaneous Velocity is expressed in m/s. If any problem contains the function of the form f(x), the instantaneous velocity is determined using the above formula.

Related Calculators
Instantaneous Velocity Calculator Instantaneous Acceleration Calculator
Instantaneous Rate of Change Calculator Calculate Velocity
 

Instantaneous Velocity Problems

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Below are some problems based on instantaneous velocity which helps to understand the formula better.

Solved Examples

Question 1: Find the Instantaneous Velocity of a particle moving along a straight line with a function x = 5t2 + 2t + 3 at time t = 3s?
Solution:
 
Given: The function is x = 5t2 + 2t + 3
Differentiating the given function with respect to t, we get Instantaneous Velocity
Vinst = $\frac{dx}{dt}$
       = $\frac{d(5t^{2} + 2t + 3)}{dt}$
       = 10t + 2
For time t = 3s, the Instantaneous Velocity is V(t) = 10t + 2
V(3) = 10(3) + 2 = 32m/s
Instantaneous Velocity for the given function is 32m/s.
 

Question 2: The motion of the car is given by the function x = 4t2 + 10t + 6. Calculate its Instantaneous Velocity at time t = 5s.
Solution:
 
Given: The function is x = 4t2 + 10t + 6.
Differentiating the given function with respect to t, we get
Vinst = $\frac{dx}{dt}$
       = $\frac{d(4t^{2} + 10t + 6)}{dt}$
       = 8t + 10.
For time t = 5s, the Instantaneous Velocity is V(t) = 8t + 10
V(5) = 8(5) + 10 = 50 m/s.
Instantaneous Velocity for the given function is 50 m/s.
 

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