Show that a body projected vertically up from the ground, the distance travelled by it in the last second of its upwards motion is an constant independent of its initial velocity

Answer and explanation:

Let be the velocity of a body projected vertically up, 1 second before it reaches its maximum height. We know, from the kinematics equations, that the distance traveled in an interval of time is equal to:

Then, in the last second, the distance traveled is equal to:

But the velocity is related to the time by the equation:

And substituting this expression in the equation above, we obtain:

It means that the distance traveled by the body in the last second of its motion is a constant, independent of its initial velocity.

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