Question

for an object in free fall, calculate the rate of change of the velocity from the first to the 100th second (metric units).

Answer 1

Answer:

The rate of change of velocity is 9.81 m/$s^2$.

Explanation:

By using the equation of motion, the velocity of any object in free fall at any instant, $v=u+gt$

Where u (constant) is the initial velocity,

$g=9.81 m/s^2$ is the acceleration due to gravity,

v= velocity at time t.

To get the rate of change of velocity, differentiating the velocity, v, with respect to time, as

$\frac {dv}{dt}=\frac{d}{dt}(u+gt) \\\\=\frac{d}{dt}u +\frac{d}{dt}(gt) \\\\=0+g\\\\=g$

$\Rightarrow \frac{dv}{dt}=9.81 m/s^2$

Hence, the rate of change of velocity is 9.81 m/$s^2$.