Instantaneous Acceleration

As we know that acceleration (a) is the rate of changing the velocity of object with time, so both are vector quantity not a scalar quantity. This is a type of force and explained by the Newton second law. This is measured in terms of meter per square of time unit. It is directly proportional to the applied net force of the constant mass body in classical mechanics.

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So mathematically it can be shown with its formula that is; a = v x t,
where, (a) is the moving body’s (a), v is the velocity, and t denotes the taken time.
Here we discuss instantaneous acceleration (IA). This can be described as the average (a) limit when the interval of time goes to zero. Or it is the (a) at a particular point of time in very short time interval approaches zero. This is very important factor in laws of mechanics.
We can answer the question that How to Find Instantaneous Acceleration by taking knowledge about the Instantaneous Acceleration Formula.  For describing the formula, we will find the value of for a moving body in a particular time period. This value of (a) at any instant of time shows the Instantaneous Acceleration Equation.


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Here we consider the particle’s velocity which moves on a curve is the time function, so the equation can be written as: the rate of change in velocity or a = limt?0 (dv /dt) or limit?0 (d2x/dt2).
The (a) can be either constant or varying accordingly. So if we plot a graph between the velocities with time then we find a straight line. This is the Instantaneous Acceleration Graph as shown below;

We can better explain it by taking some mathematical problems base on IA. For example; calculate the (a) in the time limit 0 = t = 6 for a moving particle whose velocity is t3/3 – 4t2 + 16t – 64.
As we know the formula for IA that is a = limt?0 (dv /dt) or limit?0 (d2x/dt2), so a = d/dt (t^3/3 – 4t^2 + 16t – 64),  a = d (t^3/3 – 4t^2 + 16t – 64)dt
or a = 3t^2/3 - 8t + 16
So the IA at t = 6 seconds is given by; a = limt?6 (t^2 - 8t + 16),
Or a = 36- 8 × 6 + 16
Or  a  = 36 - 48 + 16
Or a = 52-48 = 4 m/s^2.
Similar we can also take other examples like find the value of (a). Thus we can see that the (a) is a function of time.