🚲 Imagine you're on a bicycle, cycling along a straight path. Let's use this story to understand distance-time, velocity-time, and acceleration.

• First 10s: You kick-off and speed up (accelerate) to a speed of +4ms^-1. 'Positive' here means you're heading right.
• 10s to 45s: You're cruising at a steady speed of +4ms^-1.
• At 45s: You hit the brakes and come to a full stop in 5s.
• 45s to 60s: You take a quick break, completely stationary.
• 60s onwards: You decide to head back (left, hence negative velocity), picking up speed till 3ms^-1, cruise at this speed for a while, then gradually slow down to a stop at 120s.

Now, let's convert this fun ride into scientific knowledge!

Acceleration

• The gradient (slope) of a velocity-time graph gives acceleration. The direction of the slope tells you which direction you're accelerating.

• From 45s to 50s: You slowed from 4ms^-1 to 0, so the acceleration was

  (final speed - initial speed) / time taken = \( \frac {(0 - 4)}{ 5}\)  = -0.80ms^-2

• From 90s to 120s: Your speed change over time gave you an acceleration of

  \(\frac {speed\ change}{time\ taken}\) = \( \frac{3.0}{30} \) = 0.10ms^-2

Note: If the gradient of the graph is positive, the acceleration is also positive. That means, if you're slowing down while moving in the negative direction (like our bike ride back), a force is acting on you in the positive direction, slowing you down.