It took a long time for scientists to develop correct ideas about forces and motion. We will start by thinking about some wrong ideas, and then consider why Galileo, Newton and others decided new ideas were needed.

Observations and ideas

Here are some observations to think about.
- The large tree trunk shown in Figure 3.6 is being pulled from a forest. The elephant provides the - force needed to pull it along. If the elephant stops pulling, the tree trunk will stop moving.
- A horse is pulling a cart. If the horse stops pulling, the cart stops.
- You are riding a bicycle. If you stop pedaling, the bicycle will come to a halt.
- You are driving along the road. You must keep your foot on the accelerator pedal, otherwise the car will not keep moving.
- You kick a football. The ball rolls along the ground and gradually stops.
In each of these cases, there is a force that makes something move – the pull of the elephant or the horse, your push on the bicycle pedals, the force of the car engine, the push of your foot. Without the force, the moving object comes to a halt. So what conclusion might we draw?
A moving object needs a force to keep it moving.
This might seem a sensible conclusion to draw, but it is wrong. We have not thought about all the forces involved. The missing force is friction.
In each example, friction (or air resistance) makes the object slow down and stop when there is no force pushing or pulling it forwards. For example, if you stop pedaling your cycle, air resistance will slow you down. There is also friction at the axles of the wheels, and this too will slow you down. If you could lubricate your axles and cycle in a vacuum, you could travel along at a steady speed forever, without pedaling!

In the 17th century, astronomers began to use telescopes to observe the night sky. They saw that objects such as the planets could move freely through space. They simply kept on moving, without anything providing a force to push them. Galileo came to the conclusion that this was the natural motion of objects.
- An object at rest will stay at rest, unless a force causes it to start moving.
- A moving object will continue to move at a steady speed in a straight line, unless a force acts on it.
So objects move with a constant velocity, unless a force acts on them. (Being stationary is simply a particular case of this, where the velocity is zero.) Nowadays, it is much easier to appreciate this law of motion, because we have more experience of objects moving with little or no friction such as roller-skates with low-friction bearings, ice skates and spacecraft in empty space. In Galileo’s day, people’s everyday experience was of dragging things along the ground, or pulling things on carts with high-friction axles.
Before Galileo, the orthodox scientific idea was that a force must act all the time to keep an object moving – this had been handed down from the time of the ancient Greek philosopher Aristotle. So it was a great achievement when scientists were able to develop a picture of a world without friction.

The idea of inertia

The tendency of a moving object to carry on moving is sometimes known as inertia.
- An object with a large mass is difficult to stop moving – think about catching a football, compared with a less massive tennis ball moving at the same speed.
- Similarly, a stationary object with a large mass is difficult to start moving – think about pushing a car to get it started.
- It is difficult to make a massive object change direction – think about the way a fully laden supermarket trolley tries to keep moving in a straight line.
All of these examples suggest another way to think of an object’s mass; it is a measure of its inertia – how difficult it is to change the object’s motion. Uniform motion is the natural state of motion of an object.
Here, uniform motion means ‘moving with constant velocity’ or ‘moving at a steady speed in a straight line’.

Newton’s first law of motion

The findings on inertia and uniform motion can be summarised as Newton’s first law of motion:
In fact, this is already contained in the simple equation we have been using to calculate acceleration,  $F = ma$. If no resultant force acts on an object ($F = 0$), it will not accelerate ($a = 0$). The object will either remain stationary or it will continue to travel at a constant velocity. If we rewrite the equation as $a = \frac{F}{m}$
we can see that the greater the mass m, the smaller the acceleration a produced by a force F.

Top speed

The vehicle shown in Figure 3.7 is capable of speeds as high as $760 mph$, greater than the speed of sound. Its streamlined shape is designed to cut down air resistance and its jet engines provide a strong forwards force to accelerate it up to top speed.
All vehicles have a top speed. But why can’t they go any faster? Why can’t a car driver keep pressing on the accelerator pedal, and simply go faster and faster?
To answer this, we have to think about the two forces already mentioned: air resistance and the forwards thrust (force) of the engine. The vehicle will accelerate so long as the thrust is greater than the air resistance. When the two forces are equal, the resultant force on the vehicle is zero and the vehicle moves at a steady velocity. 

Balanced and unbalanced forces

If an object has two or more forces acting on it, we have to consider whether or not they are ‘balanced’ (Figure 3.8). Forces on an object are balanced when the resultant force on the object is zero. The object will either remain at rest or have a constant velocity.
We can calculate the resultant force by adding up two (or more) forces that act in the same straight line.
We must take account of the direction of each force. In the examples in Figure 3.8, forces to the right are positive and forces to the left are negative.
When a car travels slowly, it encounters little air resistance. However, the faster it goes, the more air it has to push out of the way each second and so the greater the air resistance. Eventually, the backwards force of air resistance equals the forwards force provided between the tyres and the road, and the forces on the car are balanced. It can go no faster–it has reached its top speed.

Free fall

Skydivers (Figure 3.9) are rather like cars–at first, they accelerate freely. At the start of the fall, the only force acting on the diver is his or her weight. The acceleration of the diver at the start must therefore be g. Then increasing air resistance opposes their fall and their acceleration decreases. Eventually, they reach a maximum velocity, known as the terminal velocity.
At the terminal velocity, the air resistance is equal to the weight. The terminal velocity is approximately 120 miles per hour (about $50\,m\,{s^{ - 1}}$), but it depends on the skydiver’s weight and orientation. Head-first is fastest.

Figure 3.8: Balanced and unbalanced forces.

The idea of a parachute is to greatly increase the air resistance. Then terminal velocity is reduced, and the parachutist can land safely. Figure 3.10 shows how a parachutist’s velocity might change during descent.
Terminal velocity depends on the weight and surface area of the object. For insects, air resistance is much greater relative to their weight than for a human being and so their terminal velocity is quite low. Insects can be swept up several kilometres into the atmosphere by rising air streams. Later, they fall back to Earth uninjured. It is said that mice can survive a fall from a high building for the same reason.