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# What is kinetic energy?

Learn what kinetic energy means and how it relates to work.

# What is kinetic energy?

Kinetic energy is the energy an object has because of its motion.
If we want to accelerate an object, then we must apply a force. Applying a force requires us to do work. After work has been done, energy has been transferred to the object, and the object will be moving with a new constant speed. The energy transferred is known as kinetic energy, and it depends on the mass and speed achieved.
Kinetic energy can be transferred between objects and transformed into other kinds of energy. For example, a flying squirrel might collide with a stationary chipmunk. Following the collision, some of the initial kinetic energy of the squirrel might have been transferred into the chipmunk or transformed to some other form of energy.

# How can we calculate kinetic energy?

To calculate kinetic energy, we follow the reasoning outlined above and begin by finding the work done, W, by a force, F, in a simple example. Consider a box of mass m being pushed through a distance d along a surface by a force parallel to that surface. As we learned earlier
\begin{aligned} W &= F \cdot d \\ &= m · a · d\end{aligned}
If we recall our kinematic equations of motion, we know that we can substitute the acceleration if we know the initial and final velocity—v, start subscript, i, end subscript and v, start subscript, f, end subscript—as well as the distance.
\begin{aligned} W &= m\cdot d\cdot \frac{v_\mathrm{f}^2-v_\mathrm{i}^2}{2d} \\ &= m\cdot \frac{v_\mathrm{f}^2-v_\mathrm{i}^2}{2} \\ &= \frac{1}{2}\cdot m \cdot v_\mathrm{f}^2 - \frac{1}{2}\cdot m \cdot v_\mathrm{i}^2 \end{aligned}
So, when a net amount of work is done on an object, the quantity start fraction, 1, divided by, 2, end fraction, m, v, squared—which we call kinetic energy K—changes.
start text, K, i, n, e, t, i, c, space, E, n, e, r, g, y, colon, space, end text, K, equals, start fraction, 1, divided by, 2, end fraction, dot, m, dot, v, squared
Alternatively, one can say that the change in kinetic energy is equal to the net work done on an object or system.
W, start subscript, n, e, t, end subscript, equals, delta, K
This result is known as the work-energy theorem and applies quite generally, even with forces that vary in direction and magnitude. It is important in the study of conservation of energy and conservative forces.

# What is interesting about kinetic energy?

There are a couple of interesting things about kinetic energy that we can see from the equation.
• Kinetic energy depends on the velocity of the object squared. This means that when the velocity of an object doubles, its kinetic energy quadruples. A car traveling at 60 mph has four times the kinetic energy of an identical car traveling at 30 mph, and hence the potential for four times more death and destruction in the event of a crash.
• Kinetic energy must always be either zero or a positive value. While velocity can have a positive or negative value, velocity squared is always positive.
• Kinetic energy is not a vector. So a tennis ball thrown to the right with a velocity of 5 m/s, has the exact same kinetic energy as a tennis ball thrown down with a velocity of 5 m/s.
Exercise 1a: Being in the wrong place when an African elephant—mass = 6000 kg, velocity = 10 m/s—is charging can really ruin your day. How fast would a 1 kg cannon ball travel if it had the same kinetic energy as the elephant?
Exercise 1b: How would you expect the damage done to a brick wall to differ in the event of separate collisions with the elephant and cannonball?
Exercise 2: Hydrazine rocket propellant has an energy density E, start subscript, d, end subscript of 1, point, 6, start fraction, start text, M, J, end text, divided by, start text, k, g, end text, end fraction. Suppose a 100 kg (m, start subscript, r, end subscript) rocket is loaded with 1000 kg (m, start subscript, p, end subscript) of hydrazine. What velocity could it achieve? To keep things simple, let’s assume that the propellant is burned up very quickly and that the rocket is not subject to any external forces.