Acceleration Formula with Solved Examples

Acceleration formula is given as the ratio of change in the velocity of any object travelling in space to time required for that change in velocity.

Introduction

It’s possible that moving a stopped bus will give it a quick boost and a jump start to it. Since lift begins with an upward force, this is the case. This would be acceleration as the speed increases! The frame will now accelerate.

The speed at which an entity’s velocity changes is referred to as acceleration. According to Newton’s 2nd law, the eventual effect of all impulses acting on a body is its acceleration. The rate with which an entity’s velocity varies is represented by acceleration. Moreover, acceleration is a vector quantity.

Formula of Acceleration

If we look at the formula of acceleration, according to its meaning ‘acceleration is referred as the ratio change of velocity of any object to change in time’, its formula can be written as,

a=change in velocity / change in time

SI Unit

The SI unit of any object’s acceleration is given by m/s². It is derived from its formula as change in velocity is measured by metre as a standard measurement, And the change in time time is also a time which is again measured in seconds as a standard measurement.

Three Helpful Equations of Motion

The three equations of motion are really helpful in finding the required motion of any object either the initial speed, final speed, acceleration or time. It is basically the relation among these entities.

Moreover, acceleration can also be found using these equations and thus it also comes under the formulas for acceleration.

The equations are,

1. v=u+at

2. v²=u²+2as

3. s=ut+1/2at²

Now for finding acceleration the formulas of motion can be changed as,

a=v-ut,

 a=v²-u² / 2s

and ,

a=2(s-ut) / t²  respectively.

Where,

v is the final velocity of the entity

u is the initial velocity of the entity

s is the distance travelled

a is the acceleration

And t is the time required for particular motion.

Examples,

Let us apply the acceleration formula in some situations and understand it much better about how to use it.

1. A bus has started moving in a straight direction from rest to a speed of 15 m/s. The time duration in which it reached its speed of 15 m/s is 30 seconds. Find the acceleration of the bus.

Answer:

Given is the initial speed of the bus which is 0m/s as the bus has started from rest and the final speed of the bus at which it reached is 15 m/s. As well as the time required for the bus to reach that speed of 15 m/s is 30 seconds.

Therefore,

We got,

u=0 m/s

v=15 m/s

t=30 s

Now using the first equation of motion which is,

v=u+at

Converting it in the form of acceleration as,

a=v-ut

Now simply substituting the values we know,

a=15-0 / 30

a=0.5 m/s

Which means the bus is accelerating at a speed of 0.5 m/s which is 0.5 metres for every second.