Question

A particle is moving in a circle of radius $20\text{cm}$. Its linear speed is given by $v=2t$, where $t$ is in $\text{second}$ and $v$ is in $\text{m/s}$. Find the radial acceleration at $t=3\text{s}$.

• A. $120{\text{m/s}}^2$
• B. $140{\text{m/s}}^2$
• C. $160{\text{m/s}}^2$
• D. $180{\text{m/s}}^2$

Answer 1

The correct option is D $180{\text{m/s}}^2$

The linear speed at any time ${}^{\prime }{t}^{\prime }$ is given by,
$v=2t$
$\Rightarrow {\left[v\right]}_{t=3\text{s}}=2\times 3=6\text{m/s}$
The radial acceleration at $t=3\text{s}$ will be,
$a_r=\frac{v^2}{r}=\frac{36}{0.2}=180{\text{m/s}}^2$