在本文中，我们将研究如何计算动能。动能是物体运动所产生的能量，它取决于物体的速度和质量。物体的运动方向对动能没有影响。对于一个运动的物体，动能被定义为使物体从静止加速到它的速度所需要做的净功。让我们假设一个物体从静止状态被一个恒定的净力加速。在这种情况下，加速度也是恒定的，我们可以使用“suvat”运动方程。

If the kinetic energy of the body after acceleration is  , we can find it by

where  is the size of the c***tant force, is the mass of the object,  isthe c***tant acceleration and  is the displacement.

From the equation  , we have  . Since our initial velocity is 0, then we have . Then,

这定义了物体的动能。

假设物体最初不是静止的。然后，网络完成：

.

也就是说，所做的功等于最终动能——初始动能，或者对物体所做的净功等于物体动能的变化。

But, what if the force was not c***tant? For this case, we need to use calculus. We use the calculus definition for work done, with as our net work done on the body, and as our net force:

现在，

.

应用链式法则，

然后我们得到，

If we again think of the case where the object’s initial speed was 0, we can define kinetic energy to be  when the speed of the object is  . We also end up with the situation where the work done has been used to change the kinetic energy of the body.

The result  is often referred to as the work-kinetic energy theorem. This states that the net work done on an object is equal to the object’s change in kinetic energy. Note that if the net work done on the body  , then the speed of the object reduces. In this case, the net work is done by the object.

Kinetic energy is a scalar quantity: since there is a  term, the sign of the velocity does not matter to the kinetic energy. Like work, kinetic energy is also measured in joules (J).

如何计算动能-示例

例1

求马和骑手的动能，质量分别为450公斤和70公斤，速度为18米s-1。

The horse and the rider in this example have about 84 kJ of kinetic energy

例2

质量为20 kg的物体被300 N的恒定力向前拉动，而400 N的恒定阻力则以相反的方向作用在物体上。如果物体在某一时刻以15ms-1的速度向前移动，那么再移动2m后，物体的动能是多少。

The resultant force is  . The net work done is then  .

根据功动能定理，

.

那么，

这是预料之中的：由于所作的净功与物体的运动方向相反，我们应该预料动能会减少。

例3

Show that for an object with momentum  , its kinetic energy could be given by