While reading Physics and Mechanics books it is common that we come across the word ‘acceleration’. Let us first know what this acceleration is and then move on to how to calculate acceleration. Acceleration is defined as the rate at which the velocity of an object changes. In a one dimensional motion, acceleration is described as a scalar quantity, since it depends upon velocity and velocity is a vector quantity so we require both magnitude and direction to describe acceleration of an object in motion.
In this article you will learn to calculate two types of acceleration, average acceleration and instantaneous acceleration in case of an object under linear motion. The term acceleration is commonly used with the increase in speed of an object with respect to time. Whenever the speed of the object decreases with respect to time we associate such change in speed with the term deceleration.
Acceleration takes different forms in different types of motions. In case of rotator motion two forms of acceleration such as centripetal and tangential acceleration are formed. Centripetal acceleration is due to the change in direction of velocity and tangential acceleration is due to the change in speed of the object.
Acceleration in mechanics
- In mechanics, we calculate acceleration as function of mass and force applied to an object. According to Newton’s law, the acceleration of a body is directly proportional to the force acting on the body.
This is given by the equation:
F = ma
a = F/m
Where,
- a=acceleration
- F = net force acting on the object
- m=mass of the object
Acceleration in this case is directly proportional to the net force acting on the body and inversely proportional to the mass of the body.
Calculating average acceleration:
As acceleration is the change in velocity over time, it is given by the formula,
a = (Vf – Vi)/t
OR
a = ∆ v/ ∆ t
Where,
- a = average acceleration
- Vf = final velocity
- Vi = initial velocity
- ∆ v = is the change in velocity
- t or ∆t = time elapsed or change in time
This formula can be used to calculate only the constant acceleration.
Calculating instantaneous acceleration
We calculate instantaneous acceleration of the object which changes speed constantly i.e. the object is not under constant acceleration. Instantaneous acceleration is measured over a very short time interval, hence the name. This acceleration is calculated as the limit of average acceleration as the time interval approaches zero.
Equation for this is given as,
Instantaneous acceleration is the derivative of velocity with time, but we know that velocity is the derivative of displacement, so acceleration becomes the second derivative of displacement with respect to time.
Therefore, acceleration can also be given as,
In the above formula ‘x’ is the displacement of the object. Hence, if you know the displacement of the object you can calculate the instantaneous acceleration of the object by taking the second derivative of the object with respect to time required for displacement.
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