Standing On The Shoulders Of Giants - Instantenous Velocity

Not too hard. Let's begin by finding the instantaneous rate of change from $t=2$ to $t=2.5$ . Because speed is distance over time, we'll take $\frac{\Delta h}{\Delta t}$ which is simply $20$ from $t=2$ to $t=2.5$ . Now, this is not an exact calculation, because obviously there are lots of factors to consider such as air resistance and acceleration. Because $20$ is the average speed on one side of $t=2.5$ , let's calculate the other, which is the instantaneous rate of change from $t=2.5$ to $t=3$ . This is simply $28$ . We can average these two instantaneous speeds to get a pretty close representation of the speed we want. This is simply $\frac{20+28}{2} \Longrightarrow 24$ . The closest answer given is $\boxed{24.5}$ , and we're done.

By newton's Equations of motion, $s=ut+\frac { 1 }{ 2 } a{ t }^{ 2 }$ Now take the derivative with respect to time this gives us: $\frac { ds }{ dt } =u+gt$ from given conditions, u=0, g=9.8, and t=2.5 therefore instantaneous velocity at time t=2.5s = 24.5