# Kinetic energy

Kinetic energy $$(E_{\text{k}})$$ is the energy that an object possesses due to its movement (its speed) and its mass.

Doing **work** on an object can give it kinetic energy.

To accelerate a stationary object so that it has $$100 \text{ J}$$ of kinetic energy, you need to do $$100 \text{ J}$$ of work.

Objects that are heavier or moving faster are **harder to stop**. This means they have more kinetic energy.

A car travelling at $$30 \ukmph$$ has **less** kinetic energy than a car travelling at $$60 \ukmph.$$

An object's kinetic energy can be calculated using the formula: $$$\Torange{\text{kinetic energy}}=\frac{1}{2}\times\Tblue{\text{mass}} \times \Tred{\text{speed}^{2}}$$$

Kinetic energy is also often abbreviated as $$KE$$ or $$T$$.

The formula for kinetic energy can be derived by first finding the displacement of the object in terms of the magnitude of acceleration $$a$$ when it is accelerated by a force of magnitude $$F$$ from rest to a speed $$v$$: $$$ \begin{align*} v^{2}&=u^{2}+2as\quad\quad u=0\\ \Rightarrow s&=\frac{1}{2}\left(\frac{v^{2}}{a}\right) \end{align*} $$$ We then find the work done by the force in accelerating the body from rest to that speed (which is equivalent to the kinetic energy possessed by the body): $$$ \begin{align*} W&=Fs\\ &=ma\cdot s\\ &=ma\times\frac{1}{2}\left(\frac{v^{2}}{a}\right)\\ &=\frac{1}{2}mv^{2}\\ W &=E_{k} \end{align*} $$$