Formula For Acceleration

Physics Formulas

Formula for Acceleration

It is defined as rate of change of velocity with respect to time.

acceleration formula

It is a vector quantity. Its S.I. unit is m/s2 and dimension is [LT-2]

(a) Instantaneous acceleration

Instantaneous acceleration is the limiting value of average acceleration as △t approaches to zero

formula instaneous

Instantaneous acceleration is equal the derivative of the velocity with respect to time.

Slope of the tangent on v-t graph gives the instantaneous acceleration.

Instantaneous acceleration also known as acceleration

instantaneous acceleration

formula of acceleration

When the acceleration is constant, the time interval in which change takes place.

Suppose a particle moving along x-axis has velocity v1 at time t1 and velocity v2 at time t2 average acceleration.

(b) Average acceleration

It is defined as ratio of change in velocity to the time interval in which change takes place. Suppose a particle moving along x-axis has velocity v1 at time t1 and velocity v2 at time t2 average acceleration aav is given by

average acceleration

Examples of Acceleration

Q1: A bus accelerates with an initial velocity of 10 m/s for 5s then 20 m/s for 4s finally for 15 m/s for 8s. What can be said about the average acceleration of the bus?

Ans: It is given that, the velocities of the bus at different time intervals is, v1 = 10 m/s, v2 = 20 m/s, v3 = 15 m/s

The time intervals for which the object possesses these velocities are t1 = 5s, t2 = 4s, t3 = 8s

Hence, over the interval, the total velocity can be given as the sum of these velocities.

velocities

Similarly, the total time interval can be given as the sum of these intervals.

△t = t1 + t2 + t3 = 5 + 4+ 8 = 17s

Using the above formula for average acceleration, we get.

Average Acceleration = △u /△t

 Average Acceleration = 45./17 = 2.65 m/s2

Q2: A sparrow, while going back to its nest accelerates to 6 m/s from 3 m/s in 5s. What can we say about its average acceleration?

Ans: Given : The initial velocity, vi = 3m/s

The final velocity, vf = 6m/s

Total time for which the acceleration takes place, t = 5 s

average accelerartion

Talk to Our counsellor