Acceleration is like the 'turbo boost' of motion; it's the rate at which an object's speed changes. In other words, it's how fast velocity changes. In the mathematical language of Physics, we denote acceleration as

Acceleration = \(\frac{distance}{time}\)

This is a vector, which means it has both a magnitude (size) and direction. Remember, the units for acceleration are m/s² or ms⁻² (preferably).

Let's think of it like this - If a cyclist is going at a speed of \(\frac {5m}{s,}\) and in the next second, they're at \(\frac {10m}{s}\) that's an acceleration of \(\frac {(10-5)}{1s}\) = \(\frac {5m}{s^2}\). The speed increased by 5m/s each second! 🚴💨

When we talk about the "magnitude of acceleration", we're focusing on its size, not the direction. If an object accelerates at 5ms⁻², it means every second it travels, the speed increases by 5ms⁻¹ in the direction of the acceleration. Just like when you pedal harder on your bike, you go faster in the direction you're pedaling.

Consider the Japanese N700 train, with an acceleration of 0.72ms⁻². If this train starts from rest, it would reach a speed of 0.72ms⁻¹ after one second. Two seconds in, it would be going at 1.44ms⁻¹ (0.72 + 0.72), and at 3s, it would be at 2.16ms⁻¹. So, it speeds up by 0.72ms⁻¹ every second, like our bike rider, but a bit slower!

Just like speed and velocity, we can find average acceleration and instantaneous acceleration

• Average acceleration:\(\frac {The\ overall\ change\ in\ velocity}{Time\ taken\ for\ the\ overall\ change}\)
• Instantaneous acceleration: The gradient of the tangent to a speed (or velocity) - time graph. Symbolically, this is represented as dv/dt or  \(\frac {Δv}{Δt}\)

We can use spreadsheets to model acceleration. For example, if you put acceleration in cell B1 and time increments in cells A4 to A18, you can calculate speed at each time by multiplying acceleration by the change in time. A graph can then illustrate how speed changes over time. It's just like a live race with your cyclist and the train. 🚴🚄

Formula tip! In cell B5: "=B4+$B$1*(A5-A4)" and so on for other cells, here $B$1 always refers to acceleration. By changing the value in cell B1, you can see how the graph changes!

Try this yourself! See how the cyclist and train fare against different accelerations. Ready, set, accelerate your learning! 🚀