Understanding Instantaneous Acceleration: Calculating Rate of Velocity Change at a Specific Time

instantaneous acceleration

Instantaneous acceleration refers to the rate at which an object’s velocity is changing at a specific moment in time

Instantaneous acceleration refers to the rate at which an object’s velocity is changing at a specific moment in time. It is the derivative of velocity with respect to time, or mathematically, the first derivative of velocity.

To calculate instantaneous acceleration, you need to have the velocity function, which describes the object’s velocity as a function of time. Let’s say the velocity function is denoted as v(t), where t represents time.

To find the instantaneous acceleration at a specific time, you differentiate the velocity function with respect to time (t). The derivative of v(t) gives you the acceleration function, denoted as a(t).

So, a(t) = d/dt [v(t)]

The instantaneous acceleration at a particular time can be determined by plugging that time value into the acceleration function a(t).

For example, let’s say the velocity function of an object is given by v(t) = 2t^2 + 3t + 6. To find the instantaneous acceleration at time t = 2, we differentiate v(t) with respect to t:

a(t) = d/dt [2t^2 + 3t + 6]
= 4t + 3

Now, we can find the instantaneous acceleration at t = 2 by plugging this value into the acceleration function:

a(t = 2) = 4(2) + 3
= 8 + 3
= 11

Therefore, the instantaneous acceleration at t = 2 for this particular object is 11.

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