Acceleration Formula

One may have perceived that pushing a terminally ill bus can give it a sudden start. That’s because lift provides an upward push when it starts. Here velocity changes and this is acceleration! Henceforth, the frame accelerates. Acceleration is described as the rate of change of velocity of an object. A body’s acceleration is the final result of all the forces being applied to the body, as defined by Newton’s second law. Acceleration is a vector quantity that is described as the frequency at which a body’s velocity changes.

Formula of Acceleration

Acceleration is the rate of change in velocity to the change in time. It is denoted by symbol a and is articulated as-

acceleration formula 1

The S.I unit for acceleration is meter per second square or m/s2.

If t (time taken), v (final velocity) and u (initial velocity) are provided. Then the acceleration is given by the formula
velocity in terms of acceleration

Acceleration formula 2

acceleration formula 3


  • Final Velocity is v
  • Initial velocity is u
  • Acceleration is a
  • Time taken is t
  • Distance traveled is s

Acceleration Solved Examples

Underneath we have provided some sample numerical based on acceleration which might aid you to get an idea of how the formula is made use of:

Problem 1: A toy car accelerates from 3 m/s to 5 m/s in 5 s. What is its acceleration?

Given: Initial Velocity u = 3  m/s,
Final Velocity v = 5m/s,
Time taken t = 5s.

Acceleration formula 5

acceleration formula 6

acceleration formula 7

acceleration formula 8

Problem 2: A stone is released into the river from a bridge. It takes 4s for the stone to touch the river’s water surface. Compute the height of the bridge from the water level.


(Initial Velocity) u = 0 (because the stone was at rest),
t = 4s (t is Time taken)
a = g = 9.8 m/s2, (a is Acceleration due to gravity)
distance traveled by stone = Height of bridge  = s
The distance covered is articulated by

Acceleration formula 9

s = 0 + 1/2 × 9.8 × 4 = 19.6 m/s2

Therefore, s = 19.6 m/s2


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