Understanding Instantaneous Velocity: Calculating Velocity at a Specific Moment in Time

instantaneous velocity

Instantaneous velocity refers to the velocity of an object at a specific instant in time

Instantaneous velocity refers to the velocity of an object at a specific instant in time. It is a measure of the rate of change of displacement with respect to time at a particular moment.

To calculate instantaneous velocity, we need to consider the concept of the derivative. The derivative of displacement with respect to time gives us velocity.

If we have the displacement-time function (s(t)), we can find the velocity-time function (v(t)) by taking the derivative of s(t) with respect to time.

Mathematically, this can be represented as:

v(t) = ds(t)/dt

where ds(t) represents the change in displacement over a small time interval dt.

To find the instantaneous velocity at a specific time ‘t’, we plug that value into the velocity-time function, v(t). This will give us the velocity at that instant.

It’s important to note that instantaneous velocity is different from average velocity, which is calculated by dividing the total displacement by the total time. Instantaneous velocity gives us the velocity at a particular moment, while average velocity gives us the average speed over a certain interval.

For example, let’s say we have the displacement function s(t) = 2t^2 + 3t + 1.
To find the instantaneous velocity at time t = 2, we first find the derivative of s(t) with respect to t:

v(t) = d(2t^2 + 3t + 1)/dt
= 4t + 3

Now, we plug in t = 2 into v(t):

v(2) = 4(2) + 3
= 8 + 3
= 11

Therefore, the instantaneous velocity at t = 2 is 11 units per second.

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