One might have observed that giving a terminally ill bus a push can cause it to start abruptly. This is due to the lift that provides an upward force when initiated. The change in velocity at this point leads to acceleration, resulting in the bus’s frame accelerating. Acceleration is the measure of the rate at which an object’s velocity changes. Newton’s second law defines an object’s acceleration as the net result of all forces acting upon it. Acceleration is a vector quantity that represents the frequency at which an object’s velocity changes.

### Formula of Acceleration

The acceleration formula is used to calculate the acceleration of an object, given its initial velocity, final velocity, and time taken for the change in velocity. The formula is:

Acceleration (a) = (Final velocity (v) – Initial velocity (u)) / Time taken (t)

### Acceleration Solved Examples

Let’s consider an example to understand this formula better. Suppose a car is traveling at a constant speed of 20 meters per second, and it accelerates uniformly to a final speed of 30 meters per second in 5 seconds. We can use the acceleration formula to calculate the acceleration of the car during this time.

Here are the values we have:

- Initial velocity (u) = 20 m/s
- Final velocity (v) = 30 m/s
- Time taken (t) = 5 s

Using the acceleration formula, we get:

Acceleration (a) = (Final velocity (v) – Initial velocity (u)) / Time taken (t) a = (30 m/s – 20 m/s) / 5 s a = 2 m/s²

So, the acceleration of the car during this time is 2 meters per second squared. This means that the car’s speed is increasing by 2 meters per second every second.

In physics, acceleration is often expressed in terms of gravity or g, which is the acceleration due to gravity on Earth’s surface, and is equal to approximately 9.8 meters per second squared (m/s²). Therefore, in this example, we can say that the car’s acceleration is about 0.2 times the acceleration due to gravity.

The acceleration formula is fundamental in physics and is used to calculate acceleration in various contexts, from simple mechanics to more complex problems involving motion under various forces.