Acceleration Formula with Velocity and Time

In this article, we will look at the acceleration formula with velocity and time. Before going any further let us define what is acceleration.
Acceleration is change in velocity over time
There are two ways to find the acceleration

Acceleration formula with velocity and time
acceleration formula with mass and force

In this article, we will look at the formula for acceleration with velocity and time. We use the acceleration formula with velocity and time when we do not have any knowledge of force acting on the body. We only have information about

Change in velocity
Time

Acceleration formula with velocity and time

As mentioned earlier acceleration is the change in velocity over time. So acceleration is the change in velocity divided by time. Mathematically,

If,

\(v_1\) is the initial velocity
\(v_2\) is the final velocity and
\(t\) is the time taken to reach ending or final velocity from starting or initial velocity then

Here,

acceleration \(a\) is in \(m/s^2\)
velocities \(v_f\) and \(v_i\) are in \(m/s\)
\(\Delta v\) is short form for change in velocity.
and time \(t\) is in \(seconds\)

Acceleration formula important facts

Acceleration s a vector quantity. Acceleration has both magnitude (a value) and direction
The direction of acceleration can be different from the direction of velocity.
Unit of acceleration is \(m/s^2\)
Acceleration can be negative and positive. It is negative when velocity decreases with time. It is positive when velocity increases with time.

Solved Questions on acceleration formula with velocity and time

Question 1. A bus decreases its speed from \(80\,\,m\,s^{-1}\) to \(60\,\,m\,s^{-1}\) in 5 seconds. Find the acceleration of the bus.
Solution. Here it is given that initial velocity,
\(v_i=80ms^{-1}\)and
final velocity,\(v_f=60ms^{-1}\)
Time \(t=5\,s\)
We have to calculate the acceleration from this data. Now from the acceleration formula we have
\(a=\frac{v_f-v_i}{t}\)
putting in the respective values
\(a=\frac{(60-80)ms^{-1}}{5s}=-4ms^{-2}\)
Note that the answer is negative. This negative sign indicates that velocity is decreasing with time.