Question

The velocity of the rabbit has a minimum at $t=$

• A. $17s$
• B. $12s$
• C. $14.6s$
• D. None of these

Answer 1

The correct option is C $14.6s$

As $x\left(t\right)$ and $y\left(t\right)$ is given then $V_x\left(t\right)=-0.62t+7.2$ and $V_y\left(t\right)=0.44t-9.1$.

Net velocity will be $V=\sqrt{\left(V_x\right(t){)}^2+(V_y\left(t\right){)}^2}$

Minimum of V will be minimum of $V^2$

So at t where $\frac{d\left(V^2\right)}{dt}=0$ then V will be minimum.

$\frac{d\left(V^2\right)}{dt}=2(-0.62t+7.2)\times -0.62+2(0.44t-9.1)\times 0.44$

Equating to zero value of $t=\frac{9.1\times 0.44+7.2\times 0.62}{0.44\times 0.44+0.62\times 0.62}$

$t=14.6sec$.