# Motion

by Chris Woodford. Last updated: September 4, 2014.

IIt's hard to believe, but everything in the world is in motion, all the time. Even
things that look perfectly still are packed with atoms that are
vibrating with energy. Understanding how motion works was one of the
great milestones of science and it's credited to the brilliant English physicist Sir Isaac Newton. His laws of motion were so well
stated that scientists still use them in most situations today. Let's
take a closer look at the science of moving things!

Photo: A space rocket is an impressive demonstration of Newton's laws of motion. The force of the hot exhaust gas shooting backward propels the rocket forward. The rocket isn't moving by pushing against the ground; it can move forward like this even in "empty space," confirming the essential truth of Newton's laws. Photo by courtesy of Great Images in NASA.

## Newton's laws in practice

How do those laws run in practice? Suppose you're standing on a skateboard. Unless you
kick against something, you'll stand on it forever going nowhere.
That's Newton's first law in action. Now if you kick against the
sidewalk, you start moving: your speed increases, and the harder you kick the faster you accelerate.
There's an example of Newton's second law. And what about the third
law? Kick back against the pavement and the pavement pushes you
with an equal and opposite reaction force that propels you forward.

Photo: Another example of Newton's laws: 1) The tractor stays still unless a force acts on it. 2) When this boy (and his friends, who are out of shot to the left) supply a force by pulling on the rope, the tractor accelerates toward them. 3) When the boys pull on the rope, the tractor pulls back: that's what keeps the rope taut. Does that seem confusing? Think of it this way. Before the boy's friends arrive, he pulls by himself on the rope and can't move the tractor. The boy pulls the rope to the left, the tractor pulls it to the right, the two forces balance, and the tractor goes nowhere.

## Speed

A sports car can go 50 times faster than you can walk and 8 times faster than you can
run. That's because its engine turns gasoline into power much more
quickly than your body can burn food to pump your muscles. The faster a car burns gas, the quicker it can go—the more
speed it has.

In science, we define speed as the distance something goes in a second. You can figure out a car's average speed by dividing how far it goes by how long it takes to get there. If a car is going at 100km/h (60mph), it can travel 100km (60 miles) in an hour.

This is the formula for speed:

Speed = d/t

Here, d is distance and t is time.

You can see from this that a car is a kind of time machine: you can use its speed to get somewhere more quickly. If you
go twice as fast, you can arrive in half the time. The faster you go,
the sooner you get there, and the more time you save. Of course, you
can never actually arrive before you leave—that would be taking the
science a bit far!

## Velocity

Velocity is not just another word for speed: it means your speed in a certain
direction. When a Formula-1 car races round a tight bend, its
speed stays the same, but its velocity is always changing because
it's turning and changing direction the whole time.

Suppose you drove from the North Pole to the South Pole in a straight line at 100km/h
(60mph) and then drove back again at the same speed. Your average speed would be
100km/h (60mph), but your average velocity would be zero. That's
because your velocity from South to North would be exactly opposite
the velocity from North to South and the two would cancel out.

This is the formula for velocity:

Velocity = d/t

Here again, d is distance and t is time. You'll notice this formula is the same as the formula for speed.
But remember when you have to state which direction the velocity is heading in too.

Photo: These two cars have exactly the same speed but completely different velocity, because they're
traveling in opposite directions.

## Acceleration

If you're a driver, acceleration means putting your foot down to go faster. But if
you're a scientist, acceleration also means stamping on the brakes.
That's because acceleration means any change in your
velocity. Speeding up is an acceleration, but so is slowing down—it's just a negative acceleration. And because your velocity is your
speed in a certain direction, you accelerate every time you go round
a corner, whether you change speed or not.

Photo: This car is going round a curve at constant speed, but its velocity is changing all the
time because its direction is changing. That means it's accelerating as well, even though its speed stays exactly the same!

A car is a heavy lump of metal and it takes a lot of force to get it moving, speed it up, slow
it down, or turn it round. The heavier something is, the more force
it takes to accelerate. That's why trucks take longer to accelerate
than cars, even though they have much bigger engines.

People compare cars by seeing how many seconds they take to accelerate from 0-100 km/h
(0-60 mph). If a car can go from 0-100 km/h in 5 seconds, it changes
its velocity by 100km/h in 5 seconds, so its acceleration is 20 km/h
per second. That's the same as changing your speed by 5.5
meters/second every second. Scientists write that 5.5 m/s/s or 5.5m/s2
(and say it out loud as "five point five meters per second squared").

This is the formula for acceleration:

a = v/t

Here, v is velocity and t is time.

## Momentum

An object's momentum is a measure of how much it wants to keep moving—and how long it can exert a force for when it stops. You can figure out something's momentum by multiplying its mass by its velocity:

momentum = mv

Here, m is mass and v is velocity.

If two things crash together, their total momentum is the same before and
after the collision. This is a basic law of physics called the conservation of
momentum. If a car crashes into a wall, bits of the wall start
moving—so they gain the momentum the car loses and that's what slows
it down.

Photo: If a truck has several times the mass of a car,
but moves at the same speed, it has several times more momentum.
The silver truck (top right) has twice the mass of the car and twice the momentum,
while the blue truck (bottom right) has five
times the mass of the car and five times the momentum.
If each vehicle were to crash into a brick wall and stop in
exactly the same time, it would exert a force proportional to its momentum.
So the blue truck would exert five times as much force as the car.

## Kinetic energy

It takes energy to make something move, and the faster it goes the more energy it needs.
In other words, energy feeds speed. The energy something has when
it's moving is called kinetic energy. You can figure out a
car's kinetic energy from this formula:

kinetic energy = ½mv2

Here, m is the car's mass and v is its velocity. If you double the weight
of a car (by adding a caravan on the back), you need to use twice as
much energy to go at the same speed. If you want to double your
speed, you'll need four times as much energy, because energy is
related to the square of your speed.

## What is an impulse?

Isaac Newton's second law tells us that force causes acceleration, and we can write that law as an equation:

F = m a

So the more force you supply, the more acceleration you get. But the same equation tells us that a = F / m, so
the more massive an object, the less it will be accelerated by a force of the same size. If you weigh twice
as much as a friend and I give you both the same push, your friend will accelerate twice as quickly.

Now we also know from up above that a = v / t, so we can rewrite Newton's second law like this:

F = m v / t

In other words, we can define force as the rate of change of momentum: the
more quickly something's momentum changes, the more force is acting on it.

Rearranging the equation one more time, we get:

F t = m v

The change in momentum is equal to the force acting on something multiplied by the time for which it acts,
and it's called an impulse. The impulse is simply F × t.

### The sporting impulse

Impulses are a really important concept in sport—for two reasons. Suppose you want to kick a soccer ball a long way, or hit a tennis ball really hard at your opponent. You'll need to give it lots of momentum (or energy, if you prefer) and to do that, you'll need to apply your boot
(or tennis racket) to the ball for as long as possible—with what's called a follow-through. Making
t (the time for which the force is acting) as long as possible produces a bigger change of momentum.
If you think about it, t is the only thing you can really change if you're a world-class athlete: the ball
has a constant mass (m) and you can only supply so much force (F), so the only way to maximize momentum (m v)
is to maximize the time (t) for which you apply your force.

There's another good reason why sports people try to increase the time for which they apply a force with their muscles.
Suppose you're catching a fast-moving baseball or cricket ball. It's fairly heavy and hurtling toward you at high speed, so
it has quite a lot of momentum. If you bring the ball to a halt slowly, by pulling your hands and arms into your body, you increase
the time (t), so the force your hands and arm feel (m v / t) is smaller and the ball hurts you less. Try to catch a ball
without moving your hands or arms and you're making t very small, which means m v / t is bigger and the ball will hurt you more. The same is also true of hitting a ball with a tennis racket, throwing a javelin, or applying a force with your muscles in any other way. Generally, all sports people try to apply forces with their muscles for as long as possible to reduce the impact on their body and the risk of injury.

Photo: Think sport? Think impulse! If you want to throw a ball as far as possible, you need to apply
a force with your muscles for as long as possible: you can't change the mass (m) of the ball, but you can maximize
time (t) as well as the force (F) to produce as big a velocity (v = F t / m) as possible. Photo by Jon Dasbach courtesy of US Navy.