Instantaneous Velocity Formula

Instantaneous velocity is defined as the velocity of an object at a particular Iinstant. Here, instantaneous velocity can be calculated as the limit of average velocity, where the time interval approaches zero. Mathematically, it is expressed as the derivative of the position function with respect to time.

Formula for Instantaneous Velocity 

Instantaneous velocity (v) can be represented as:

Where,

• v is the instantaneous velocity at the time

• Δx is the change in position (displacement),

• Δt is the change in time.

This formula pretty much says how much the position changes in an infinitesimally small amount of time.

Solved Problems

Problem 1: Determine the Instantaneous Velocity of a particle moving along a straight line for a time of t = 3s using the given function x = 5t2 + 2t + 3.

Solution: 

Given that the function is x = 5t2 + 2t + 3 

Distinguish the given function concerning t, we obtain Instantaneous Velocity

For time t=3s, the instantaneous velocity is 

V(t)= 10t + 2

V(3)=10(3)+ 2

V(3) =32 m/s

The instantaneous Velocity for the given function is 32m/s.

Problem 2: The motion of the car is provided by the function x = 4t2 + 10t + 6. Compute its Instantaneous Velocity at time t = 5s.

Solution:

Given: The function is x = 4t2 + 10t + 6.

Differentiating the provided function with respect to t, we get

For time t = 5s Instantaneous Velocity is given by,

V(t) = 8t + 10

V(5) = 8(5) + 10

V(5)= 50 m/s.

So for the known function, Instantaneous Velocity = 50 m/s.

 

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