Mathematics

The key is recognizing that instantaneous velocity is the derivative $s'(t)$, but you'll need to handle a subtle issue: the derivative of $\sqrt{t}$ involves a fractional exponent, and at $t=0$ the slope becomes undefined in a specific way. Rewrite $s(t)=t^{1/2}$, apply the power rule to find $s'(t)$, then evaluate the limit as $t \to 0^+$ to see what happens to the instantaneous rate of change right at the start.

The key is recognizing that instantaneous velocity is the derivative $s'(t)$, but you'll need to handle a subtle issue: the derivative of $\sqrt{t}$ involves a fractional exponent, and at $t=0$ the slope becomes undefined in a specific way. Rewrite $s(t)=t^{1/2}$, apply the power rule to find $s'(t)$, then evaluate the limit as $t \to 0^+$ to see what happens to the instantaneous rate of change right at the start.