Calculus is really important when it comes to understanding how fast racing cars go. It helps us see how a car's speed changes over time.

When a car speeds up, we use something called a derivative. This simply means we’re looking at how much things are changing.

Key Ideas:

• Velocity is a fancy word for how fast the car is moving. It comes from the car's position. If we say the position is $s(t)$, then velocity is $v(t) = \frac{ds}{dt}$. This means we are looking at how the position changes over time.

• Acceleration tells us how quickly the speed is changing. It's the derivative of velocity: $a(t) = \frac{dv}{dt}$.

Example:

Let’s say a race car's position is given by $s(t) = 5t^2$. If we find the velocity using calculus, we get $v(t) = \frac{ds}{dt} = 10t$. This means the car speeds up more as time goes on.

By using calculus, we can guess how well a car will perform based on different things, like how smoothly it cuts through the air and what the track is like!