Motion with constant acceleration.

Step 1 of 4

Before the fan switches on

The cart is at rest on the track. In a moment the fan on top of it will switch on and push it with a constant force. As it moves, the cart leaves a mark on the track every half second, like a strobe photograph.

Predict what will happen to the gaps between the marks, and only then watch.

Step 2 of 4

Why the gaps grow

A constant force gives a constant acceleration, $a = \dfrac{F}{m}$⁠. Constant acceleration means the speed goes up by the same amount every second: $v = a t$⁠.

If the speed keeps growing, then in each half second the cart covers more ground than in the half second before. Starting from rest, the gaps grow in the ratio $1 : 3 : 5 : 7$⁠, and the total distance grows with the square of the time:

$x = \tfrac12 a t^2$⁠

Try it: change the Fan push and the Cart mass. A stronger push or a lighter cart gives a bigger acceleration, and the marks spread apart faster.

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Step 3 of 4

How far in two seconds

Now the push and the mass are fixed. Use $a = \dfrac{F}{m}$⁠ and $x = \tfrac12 a t^2$⁠ to work out the distance. You can answer in metres or in centimetres.

Step 4 of 4

In summary

• A constant net force gives a constant acceleration, $a = \dfrac{F}{m}$⁠.
• With constant acceleration from rest, the speed grows in step with time, $v = a t$⁠, and the distance grows with the square of time, $x = \tfrac12 a t^2$⁠.
• In the next lesson you will see that the vertical motion of a launched ball is exactly this kind of motion, with $g$⁠ in place of $a$⁠.