Understanding Instantaneous Velocity and How to Calculate It

instantaneous velocity

Instantaneous velocity is the rate of change of an object’s displacement with respect to time at a specific instant or moment

Instantaneous velocity is the rate of change of an object’s displacement with respect to time at a specific instant or moment. It represents the object’s speed and direction at that particular point in time.

To compute the instantaneous velocity, we can use the concept of calculus and take the derivative of the object’s displacement function with respect to time. Let’s assume that the object’s displacement is given by the function “s(t)”, where “s” represents the displacement and “t” represents time.

The derivative of the displacement function with respect to time is denoted as “ds/dt” or “s'(t)”. This derivative represents the instantaneous velocity at any given time “t”.

Mathematically, the formula for instantaneous velocity is:

v(t) = ds/dt = s'(t)

Alternatively, we can interpret this formula as the slope of the tangent line to the displacement-time graph at that specific time “t”. The tangent line represents the object’s velocity at that instant.

To calculate the instantaneous velocity at a specific time “t”, we can differentiate the displacement function. If the displacement function is already given, we can simply take the derivative of that function with respect to time and substitute the desired time value “t” in the resulting derivative equation.

For example, let’s say the object’s displacement function is given by:

s(t) = 3t^2 + 2t + 5

To find the instantaneous velocity at time “t = 2”, we first differentiate the displacement function:

v(t) = ds/dt = 6t + 2

Then, substitute “t = 2” into the derivative function:

v(2) = 6(2) + 2
v(2) = 12 + 2
v(2) = 14

Therefore, the instantaneous velocity of the object at time “t = 2” is 14 units per time.

It’s important to note that instantaneous velocity gives us the velocity at a specific moment in time, while average velocity represents the total displacement over a given time interval.

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