Energy is the “amount of motion”. Suppose that two identical cars are racing down a road; the faster car has more energy. Suppose that a truck and a small car are travelling side by side along the road and at the same speed; the truck is heavier and therefore has more energy. It is harder to stop. Thus, in moving objects, more speed or more mass means more energy. As a car accelerates or as we push a body along, it gains more energy.
Einstein discovered that a moving object weighs more than the same object at rest; that is, an object with more energy also has more mass. As the speed of an object increases, its mass increases. As objects move faster and faster and approach the speed of light, their mass becomes nearly infinite. This effect is called “relativistic mass increase”. There are various ways of describing this but the one adopted here is the simplest and most common.
Energy can also be stored inside objects. Suppose we hold the ends of an elastic band in our hands. As we move our hands apart, they have motion and thus energy. As the band stretches to its limit, our hands slow down and the band absorbs their energy. The energy or motion is clearly in the band. If we relax and let the band pull on our hands, they will move together again. This inward motion has the energy that was stored in the band. Thus the band is a device for absorbing, storing and releasing energy.
Stored energy also has mass. When the elastic band is stretched or a spring is compressed it weighs more. Likewise, a new battery weighs slightly more than a used battery. Like time dilation and length contraction, this mass increase is not noticeable in everyday life. The extra mass is only significant when bodies move at enormously high speeds. The motion of our hands stored in the elastic band is so slow that no device yet invented is capable of measuring the mass increase.
To summarize, with faster speeds bodies weigh more, that is, they have more mass. More precisely: Relativistic mass increase: Assume an apparatus at rest or moving at a steady speed in the same direction is used to measure the mass of passing bodies. A given body that is measured at several speeds will have higher masses at faster speeds.