Understanding Instantaneous Acceleration: Definition, Calculation, and Example

instantaneous acceleration

Instantaneous acceleration refers to the rate at which an object’s velocity changes at a specific point in time

Instantaneous acceleration refers to the rate at which an object’s velocity changes at a specific point in time. It measures how quickly an object’s speed or direction changes at that precise moment.

Mathematically, instantaneous acceleration is defined as the derivative of velocity with respect to time. This means that you take the derivative of the velocity function to find the instantaneous acceleration function.

Let’s say we have an object with velocity function v(t). To find the instantaneous acceleration at a certain time t, we take the derivative.

The derivative of v(t) with respect to time gives us: a(t) = dv(t)/dt.

This equation represents the instantaneous acceleration at any given time t.

For example, let’s say we have a car moving along a straight road, and its velocity at time t is given by the function v(t) = 5t^2 – 10t + 3. To find the instantaneous acceleration at time t=2, we take the derivative of v(t).

Taking the derivative of v(t) gives us: a(t) = d(5t^2 – 10t + 3)/dt.

Differentiating each term with respect to t, we get: a(t) = 10t – 10.

Now, substituting t=2 into the equation, we find the instantaneous acceleration at time t=2: a(2) = 10(2) – 10 = 20 – 10 = 10.

Therefore, the instantaneous acceleration of the car at time t=2 is 10 units per second squared.

In summary, instantaneous acceleration represents how an object’s velocity changes at a specific point in time. It is determined by taking the derivative of the velocity function with respect to time.

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