# Acceleration

### Acceleration

Whenever we are getting late for office and your driver is driving you to office, you ask your driver to hurry up and in response to that, you feel the car going faster. This is called acceleration. So, what is acceleration?

Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object accelerating if it is changing its velocity.

What is Acceleration?

Acceleration of an object is defined as its rate of change of velocity at that instant. It is denoted as “a” and the units are m/sec². Any object experiencing an unbalanced force, constant or variable show acceleration (or) Any object undergoing a change in its velocity either magnitude or direction or both is said to be accelerated.

Acceleration Formula:

$$Acceleration(a)\,=\,\frac{Change\,\,in\,\,velocity}{Time\,\,taken}$$.

If time taken (t), final velocity (v) and Initial velocity (u) are provided. Then the acceleration is given by formula:

v = u + at

v² = u² + 2as

s = ut + ½ at²

Where,

Final velocity = v

Initial velocity = u

Acceleration = a

Time taken = t

Distance travelled = s.

How to find the Acceleration?

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

Solution: Given,

Initial Velocity (u) = 0 m/sec² (Because the stone was at rest)

Time taken (t) = 5 sec

a = g = 9.8 m/sec²

Distance travelled by stone = height of the bridge = s

Using Kinematic Relation:

s = ut + ½ at²

s = 0 x 5 + ½ x 9.8 m/sec² x (5 sec)² = 122.5 m

∴ Height of the bridge from the water level is 122.5 m.