Question

A particle moves in a circle of radius $2\text{cm}$ at a speed given by $v=4t$, where $v$ is in $\text{cm/s}$ and $t$ is in seconds. Then

• A. tangential acceleration at $t=1\text{s}$ is $4{\text{cm/s}}^2$
• B. total acceleration at $t=1\text{s}$ is $4\sqrt{2}{\text{cm/s}}^2$
• C. total acceleration at $t=1\text{s}$ is $4\sqrt{5}{\text{cm/s}}^2$
• D. tangential acceleration at $t=1\text{s}$ is $5{\text{cm/s}}^2$

Answer 1

Answer: (A), (C)

The correct options are
A tangential acceleration at $t=1\text{s}$ is $4{\text{cm/s}}^2$
C total acceleration at $t=1\text{s}$ is $4\sqrt{5}{\text{cm/s}}^2$

Tangential acceleration
$\begin{array}{c}{a}_t=\frac{dv}{dt}\\ a_t=\frac{d}{dt}\left(4t\right)=4cm/s^2\\ \text{Now for acceleration},\\ a_c=\frac{v^2}{R}=\frac{(4{)}^2}{2}=8\\ \Rightarrow a=\sqrt{a_t^2+a_c^2}\\ =\sqrt{(4{)}^2+(8{)}^2}=4\sqrt{5}m/s^2\end{array}$