# How fast must a 1800 kg car move to have the same momentum as the 2500 kg bus travelling at 25m/s ?

This kinetic energy calculator is a tool that helps you assess the energy of motion. It is based on the kinetic energy formula, which applies to every object in a vertical or horizontal motion.

The following article will explain:

• What is kinetic energy;
• How the kinetic energy formula is used;
• The definition of kinetic energy;
• What are some common kinetic energy units;
• What is the difference between potential and kinetic energy;
• How the work-energy theorem can be applied; and
• How the dynamic pressure and the kinetic energy equations relate to each other.

The encyclopedia provides the following definition of kinetic energy:

The kinetic energy of an object is the energy it possesses due to its motion. We define it as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains its kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.

Kinetic energy is the energy of an object in motion. It provides information about how the mass of an object influences its velocity. Let's take an example. If you put the same engine into a lorry and a slick car, the former cannot achieve the same speed as the latter because of its mass. Another example of kinetic energy is the human punch force, where the energy accumulates in the body and transfers through the punch. You can easily find it out by using our kinetic energy calculator.

The kinetic energy formula defines the relationship between the mass of an object and its velocity. The kinetic energy equation is as follows:

KE = 0.5 × m × v²,

where:

• m - mass; and
• v - velocity.

With the kinetic energy formula, you can estimate how much energy is needed to move an object. The same energy could be used to decelerate the object, but keep in mind that velocity is squared. This means that even a small increase in speed changes the kinetic energy by a relatively high amount.

How about you give our kinetic energy calculator a try? This tool does any and every calculation for you after typing the mass and velocity of an object. It even works in reverse, just input any two known variables, and you will receive the third! If you don't know the object's speed, you can easily calculate it with our velocity calculator.

You should be aware, however, that this formula doesn't take into account relativistic effects, which become noticeable at higher speeds. If an object is moving faster than 1% of the speed of light (approximately 3,000 km/s, or 3,000,000 m/s), you should use our relativistic kinetic energy calculator.

The units of kinetic energy are precisely the same as for any other type of energy. The most popular and commonly used kinetic energy units are:

• Joule (J), equivalent to kg · m² / s² - SI unit;
• Foot-pound (ft·lb) - imperial unit;
• Electronvolt (eV);
• Calorie (cal);
• Watt-hour (Wh).

We can easily convert all of these kinetic energy units into one another with the following ratios:
1 J = 0.7376 ft·lb = 6.242·10¹⁸ eV = 0.239 cal = 2.778·10⁻⁴ Wh.

As you can see, depending on the scale, they may differ by a significant number of orders of magnitude, so it's convenient to use scientific notation or express them with some prefix like kilo- (kcal, kWh), Mega- (MeV), etc. Anyway, you don't need to worry about the units while using our kinetic energy calculator; you can choose whichever you like by clicking on the units, and the value will be immediately converted.

Potential energy refers to the gravitational pull exerted on an object relative to how far it has to fall. When the object gains altitude, its potential energy increases. If you want to check what potential energy is and how to calculate it, use our potential energy calculator.

It turns out that kinetic energy and the amount of work done in the system are strictly correlated, and the work-energy theorem can describe their relationship. It states that we can convert the work done by all external forces into a change of kinetic energy:

W = ΔKE = KE₂ – KE₁.

Actually, there are several types of kinetic energies. We can distinguish:

1. Translational kinetic energy - the most well-known type. It's related to the motion of an object traveling in a particular direction and the distance it covers in a given time. This is the kind of energy that you can estimate with this kinetic energy calculator.

2. Rotational kinetic energy - as the name suggests, it considers a body's motion around an axis. Check Omni's rotational kinetic energy calculator to learn the exact formula.

3. Vibrational kinetic energy - can be visualized as when a particle moves back and forth around some equilibrium point, approximated by harmonic motion. Depending on the structure, it can be shown as stretching, twisting, or bending.

At the microscopic scale, all of these kinetic energy examples are manifestations of thermal energy, which increases as the temperature rises.

The expression of the dynamic pressure (caused by fluid flowing) is the following:

p = ρ × v² / 2.

It looks very similar to the kinetic energy equation because we replace mass with density, which isn't coincidental. The other name for dynamic pressure is kinetic energy per unit volume; analogically, density is the mass contained in a particular volume. With just a pinch of imagination, you can use our kinetic energy calculator to estimate the dynamic pressure of a given fluid. If you replace mass in kg with density in kg/m³, then you can think about the result in J as the dynamic pressure in Pa.

You're sitting in class, and your teacher tells you that the kinetic energy of an object equals 1 J. What do you think - is that a lot, or not really? The key information is what kind of object we are talking about. Let's take a look at some computational kinetic energy examples to get to grips with the various orders of magnitude:

1. Some of the highest energy particles produced by physicists (e.g., protons in Large Hadron Collider, LHC) reach the kinetic energy of a few TeV. It is said to be comparable to the kinetic energy of a mosquito. It's impressive when you realize the enormous number of molecules in one insect. However, if we work out the value in joules, then the outcome is in the order of 1 μJ. Based on that, an individual particle with the kinetic energy of 1 J is extraordinarily high-energy and will surely not be produced by humanity any time soon.

2. Let's consider a bullet of mass 5 g, traveling at a speed of 1 km/s. Its kinetic energy equals 2,500 J, way above 1 J because of the considerable velocity. That's the reason why bullets cause a lot of damage while hitting targets. Use the kinetic energy calculator to find out how fast the same bullet will have to be traveling at to get its energy to 1 J. It's a velocity of about 20 m/s. Well, it will still hurt when it impacts a body, but it definitely won't cause anything worse than a bruise.

3. The ship weighs 50,000 tons and can move at the speed of 10 knots. We can always use speed converter to find that it's around 5.1 m/s. Its kinetic energy is then roughly 661 MJ. That number is mainly a consequence of its impressive mass.

Kinetic energy can be defined as the energy possessed by an object or a body while in motion. Kinetic energy depends on two properties: mass and the velocity of the object.

The formula to calculate the kinetic energy of an object with mass m and traveling at velocity v is
KE = 0.5 × m × v²

To calculate kinetic energy:

1. Find the square of the velocity of the object.
2. Multiply this square by the mass of the object.
3. The product is the kinetic energy of the object.

An average cricket ball weighs 165 g. Therefore, the kinetic energy of the cricket ball is KE = 0.5 × m × v² = 133.5 J.

A 450 g or ~1 lb football traveling towards the field goal at about 38.4 m/s or 126 ft/s has a kinetic energy of 331.7 J.

Momentum is how much something wants to keep moving in the same direction.

This truck would be hard to stop ...

... it has a lot of momentum.

Faster? More momentum!
Heavier?
More momentum!

Momentum is mass times velocity.
The symbol is p:

p = m v

### Example: What is the momentum of a 1500 kg car going at highway speed of 28 m/s (about 100 km/h or 60 mph)?

p = m v

p = 1500 kg × 28 m/s

p = 42,000 kg m/s

The unit for momentum is:

• kg m/s (kilogram meter per second), or
• N s (Newton second)

They are the same! 1 kg m/s = 1 N s

We will use both here.

More examples:

Mass Speed Momentum 7.5 g 0.0075 kg 1000 m/s 0.0075 × 1000 = 7.5 kg m/s 57 g 0.057 kg 50 m/s 0.057 × 50 = 2.85 kg m/s 16 oz 0.45 kg 100 km/h 28 m/s 0.45 × 28 = 12.6 kg m/s 22 oz 0.6 kg 3 m/s 0.6 × 3 = 1.8 kg m/s 400 g 0.4 kg 7 m/s 0.4 × 7 = 2.8 kg m/s 80 kg 9 km/h 2.5 m/s 80 × 2.5 = 200 kg m/s 1500 kg 100 km/h 28 m/s 1500 × 28 = 42,000 kg m/s

Momentum has direction: the exact same direction as the velocity.

But many examples here only use speed (velocity without direction) to keep it simple.

### Animation

Play with momentum in this animation.

## Impulse

Impulse is change in momentum. Δ is the symbol for "change in", so:

Impulse is Δp

Force can be calculated from the change in momentum over time (called the "time rate of change" of momentum):

F = Δp Δt

### Example: You are 60 kg and run at 3 m/s into a wall. The wall stops you in 0.05 s. What is the force? The wall is then padded and stops you in 0.2 s. What is the force?

First calculate the impulse:

Δp = m v

Δp = 60 kg x 3 m/s

Δp = 180 kg m/s

Stopping in 0.05 s:

F = Δp Δt

F = 180 kg m/s 0.05 s = 3600 N

Stopping in 0.2 s:

F = Δp Δt

F = 180 kg m/s 0.2 s = 900 N

Stopping at a slower rate has much less force!

• And that is why padding works so well
• And also why crash helmets save lives
• And why cars have crumple zones

 Start with: F = ma Acceleration is change in velocity v over time t: F = m Δv Δt Rearrange to: F = Δmv Δt And Δmv is change in momentum: F = Δp Δt

## Impulse From Force

We can rearrange:

F = Δp Δt

Into:

Δp = F Δt

So we can calculate the Impulse (the change in momentum) from force applied for a period of time.

Δp = F Δt

Δp = 300 N × 0.02 s

Δp = 6 N s

## Momentum is Conserved

Conserved: the total stays the same (within a closed system).

Closed System: where nothing transfers in or out, and no external force acts on it.

### In our Universe:

• Mass is conserved (it can change form, be moved around, cut up or joined together, but the total mass stays the same over time)
• Energy is conserved (it also can change form, to light, to heat and so on)
• And Momentum is also conserved!

Note: At an atomic level Mass and Energy can be converted via E=mc2, but nothing gets lost.

## Momentum is a Vector

Momentum is a vector: it has size AND direction.

Sometimes we don't mention the direction, but other times it is important!

### One Dimension

A question may have only one dimension, and all we need is positive or negative momentum:

### Two or More Dimensions

Questions can be in two (or more) dimensions like this one:

### Example: A pool ball bounces! It hits the edge with a velocity of 8 m/s at 50°, and bounces off at the same speed and reflected angle. It weighs 0.16 kg. What is the change in momentum?

Let's break the velocity into x and y parts. Before the bounce:

• vx = 8 × cos(50°)   ...going along
• vy = 8 × sin(50°)   ...going up

After the bounce:

• vx = 8 × cos(50°)   ...going along
• vy = 8 × −sin(50°)   ...going down

The x-velocity does not change, but the y-velocity changes by:

Δvy = (8+8) × sin(50°)
= 16 × sin(50°)

And the change in momentum is:

Δp = m Δv

Δp = 0.16 kg × 16 × sin(50°) m/s

Δp = 1.961... kg m/s

p = m v
Momentum is mass times velocity

is not the full story!

It is a wonderful and useful formula for normal every day use, but when we look at the atomic scale things don't actually collide. They interact from a distance through electro-magnetic fields.

And the interaction does not need mass, because light (which has no mass) can have momentum.

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