Linear Acceleration Formula

Before defining the term linear acceleration, it is necessary to first clarify that it is a term related to the object in movement. Acceleration is the measure of how quickly the velocity of any moving object changes. Therefore, the acceleration is the change in the velocity, divided by the time. Acceleration is having the magnitude as well as the direction. This article will explain the concept of acceleration with a linear acceleration formula. Let us learn it!

Linear Acceleration Formula

What is the linear acceleration?

An object that is moving in a straight line will be accelerating if its velocity is increasing or decreasing during a given period of time. Acceleration can be either positive or negative depending on whether the velocity is increasing or decreasing. A vehicles’ motion can help to explain the linear acceleration. The speedometer in the vehicle measures the velocity.

One may have observed that pushing a terminal bus can give it a sudden start. This is because the lift provides an upward push when it starts. Here Velocity changes and this will cause the acceleration. Therefore the acceleration will be described as the rate of change of velocity of an object.

A body’s acceleration will be the final result due to all the forces being applied to the body. We also describe it by Newton’s Second Law. Acceleration is a vector quantity that is described as the frequency at which the object’s velocity changes.

The formula for Linear Acceleration:

Acceleration is the rate of change in the velocity towards the time change. We denote it by symbol a,  and compute it as-

Linear Acceleration = \(\frac {Change in Velocity}{ Time Taken}\)

Its unit is meter per second squared or m \(s^{-2}\).

If t (time is taken), v (final velocity) and u (initial velocity) are provided.

Then the acceleration formula:

• v = u+at
• v² = u² + 2as
• \(s = ut + \frac{1}{2} at^2\)

Where,

v	Final Velocity
u	Initial velocity
a	acceleration
t	time taken
s	distance traveled

Linear acceleration is also a component, where is no radial component of acceleration. Also, linear acceleration does not change direction only changing velocity, which is the increase or decreases the velocity of an object.

Solved Examples

Q.1: A car accelerates from 3 m per sec to 5 m per sec in 5 seconds. What will be the acceleration?

Solution:

Given parameters:

Initial Velocity u = 3m per s

Final Velocity v = 5 m per s,

Time taken t = 5 s.

Acceleration, a = \(\frac{v – u}{t}\)

A = \(\frac {5-3}{5}\)

A = 0.4 m per sec²

Q.2: A stone is released into the river from some bridge. It takes 4 seconds for the stone to touch the river’s water surface. Find out the height of the bridge from the water level.

Solution:

(Initial Velocity) u = 0, (because the stone was at rest),

t = 5 s (t is Time taken)

a = g = \(9.8 m s^{-2}, (g is Acceleration due to gravity)\)

Distance travelled by the stone will be the height of bridge  = s

The distance covered is:

s = ut + \(\frac{1}{2} at^2\)

=\( 0 \times 5  + \frac{1}{2} 9.8 \times 5^2\)

= \(0 + \frac{1}{2} \times 9.8^2 \times 5\)

= 122.5 m.