The distance travelled by an object in time $t$ is given by $s=(2.5) t^{2}$. The instantaneous speed of the object at $\mathrm{t}=5 \mathrm{~s}$ will be:

The distance traveled by an object in time $t$ is given by the equation $s = (2.5)t^2$. To find the instantaneous speed at a specific time, we need to find the first derivative of the distance function with respect to time, which gives us the velocity function: <br/><br/> $v(t) = \frac{ds}{dt}$ <br/><br/> Differentiating the given equation with respect to $t$: <br/><br/> $v(t) = \frac{d}{dt} (2.5)t^2 = 2(2.5)t = 5t$ <br/><br/> Now, we can find the instantaneous speed at $t = 5 \mathrm{~s}$ by plugging the value into the velocity function: <br/><br/> $v(5) = 5(5) = 25 \mathrm{~m/s}$ <br/><br/> The instantaneous speed of the object at $t = 5 \mathrm{~s}$ is $25 \mathrm{~m/s}$.