Acceleration and Deceleration

In I/GCSE Physics, for the Acceleration formula we are simply building off the knowledge we have already learnt. The formula for Acceleration is **Δv/Δt**, ‘**Δ**’ is the Greek letter delta, it is standard notation in Physics and stands for ‘change in’. Therefore, this formula is equal to ‘**Change in Velocity ÷ Change in Time**’.

In order to prove this formula we must first find how to calculate the **difference** between our **starting velocity** and our **final velocity**. There are two ways of doing this: first, you can simply count up from the starting velocity to the final velocity whilst also counting the amount of numbers you are counting. Or, secondly, you can subtract the starting velocity from the final velocity and this will also show you the amount of **increase (or decrease)**.

The second method is actually how the GCSE textbooks write the formula for Acceleration; **v-u/t** **(v = final velocity, u = starting velocity, t = time)**. So you may want to write it like that if you are studying for GCSE.

**Example**

You are driving at **5m/s**, you accelerate for **10 seconds** and are now driving at **15m/s**. Using our prior knowledge we can work out the acceleration mentioned in the I/GCSE physics.

- Write out your formula:
**v-u/t**(**v = 15m/s**, our final velocity.**u = 5m/s**, our starting velocity.**T = 10 seconds**is the amount of time spent accelerating). - Now we substitute our values in and find the change in speed:
**15m/s - 5m/s = 10m/s (Δv)**, - Then divide by the amount of time spent accelerating:
**10m/s ÷ 10s (Δt). = 1m/s Acceleration**.

This equals **Acceleration**; the **rate** at which the **speed** or **velocity increases**. Hopefully you can see the logic behind it now. Extra things to note include: when the **value/rate** at which the speed or velocity changes is **negative** (meaning it is **decreasing**) it is referred to as **Deceleration**. A change in **Acceleration/Deceleration** can also be a change in **direction** because a change in direction is a change in **velocity**. Of course, this only applies to velocity.

Finally, sometimes you will see Acceleration written as **d/s^square (Distance ÷ Seconds × Seconds)**, why is this? Well, let’s think about this mathematically: **Speed = Distance ÷ time**, therefore **v/s = d/s^square**, makes sense, right? This is technically a formula for Acceleration, but in order for this to be correct the value of the seconds we divided by first must be the same as the value of the seconds we divided by next and that is rarely the case. This is the formula can cause great confusion, and it is for that reason that I recommend you only learn the formula below:

*Formula for Acceleration: Δv/Δt (Change in Velocity ÷ Change in Time)*

End of this topic!