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

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

Step-by-step 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}=(d)/(dt)(u+gt) \\\\=(d)/(dt)u +(d)/(dt)(gt) \\\\=0+g\\\\=g`

`\Rightarrow (dv)/(dt)=9.81 m/s^2`

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