Question

A body of mass $1 \, kg$ starts moving from rest at $t \, = \, 0$ , in a circular path of radius $8 \, m$ . Its kinetic energy varies as a function of times as $KE \, =2t^{2}$ Joules, where $t$ is in seconds. Then

• A. Tangential acceleration = $4ms^{- 2}$
• B. Power of all forces at $t=2s$ is $8W$
• C. First-round is completed in $2s$ .
• D. Tangential force at $t=2s$ is $4N$ .

Answer 1

Answer: (B)

$\frac{1}{2}mv^{2}=2t^{2}$
$v^{2}=4t^{2}\Rightarrow v=2t$
$a_{\text{t}}=\frac{\text{d} \textit{v}}{\text{d} \textit{t}}\Rightarrow a_{\text{t}}=2\text{m s}^{- 2}$
$F_{\text{t}}=ma_{\text{t}}\Rightarrow F_{\text{t}}=2\text{N}$
Power will be inverted only by tangential force
$P=\left(\vec{F}_{ t }+\vec{F}_{ c }\right) \cdot \vec{V}$ since $F_{ c } \perp V \& F_{ t } \| V$
$P=F_{ t } V \quad \Rightarrow \quad P=2 \times 2 t$
$\Rightarrow \quad P=4 t \quad \Rightarrow \quad P=8 W$