Push harder, go faster: force, mass and acceleration

Push an empty shopping trolley. Whoosh, off it goes! Now push a trolley piled high with shopping. It moves slowly and it takes much more effort. What is going on?

What is acceleration?

When something speeds up, slows down or changes direction, we say it accelerates.

Acceleration is how quickly the speed changes. A car that goes from 0 to 10 m/s in 5 seconds speeds up by 2 m/s every second. We say its acceleration is 2 m/s² ("2 metres per second per second").

A quick way to think about it: speed tells you how fast you are going, and acceleration tells you how fast your speed is changing.

Two things change acceleration

1. The size of the force. A harder push gives a bigger acceleration. Push the trolley twice as hard, and it speeds up twice as fast.

2. The mass of the thing. The more mass, the smaller the acceleration for the same push. A full trolley has more mass, so the same push makes it speed up less.

Newton's second law

This is Newton's second law of motion. In words:

The bigger the force, the bigger the acceleration. The bigger the mass, the smaller the acceleration.

And as a short formula:

force = mass × acceleration

or, turning it round:

acceleration = force ÷ mass

The units fit together neatly. A force of 1 newton is exactly the push that makes a 1 kg object speed up by 1 m/s every second.

Two worked examples

1. A 10 N push on a 2 kg trolley. Acceleration = 10 ÷ 2 = 5 m/s².

2. The same 10 N push on a 5 kg trolley. Acceleration = 10 ÷ 5 = 2 m/s².

Same push, but the heavier trolley speeds up less than half as much.

It explains everyday things

• A football flies off at high speed when you kick it. A bowling ball hit with the same kick barely moves. Same force, much bigger mass.
• A bike speeds up faster than a lorry, if both use the same force.
• A rocket is mostly fuel at the start. As the fuel burns off, its mass drops, so the same engine makes it accelerate more and more.

Why gravity treats everything alike

Remember that a heavy ball and a light ball fall together? Now you can see why.

Gravity pulls a heavy ball with a bigger force. But the heavy ball also has a bigger mass, so it needs a bigger force to speed up. The two effects cancel exactly. The result is that everything falls with the same acceleration, which is 9.8 m/s² on Earth. Each second of falling, an object gets 9.8 m/s faster.

After 3 seconds of falling without air, the speed would be about 29 m/s.

Back to Launch Lab

When you set a speed in Launch Lab, you are choosing how hard the launcher pushes the ball. Gravity then accelerates the ball downward at 9.81 m/s² on Earth, but only 1.62 m/s² on the Moon. That is why the ball flies so much farther there.