Question

A particle moves in a circle of radius $1.0cm$ with a speed given by $v=2t$ where $v$ is in $cm/s$ and $t$ in seconds. Find the magnitude of net acceleration at $t=1s$.

• A. $\sqrt{5}m{s}^{-2}$
• B. $2\sqrt{5}m{s}^{-2}$
• C. $3\sqrt{5}m{s}^{-2}$
• D. $3\sqrt{3}m{s}^{-2}$

Answer 1

The correct option is B $2\sqrt{5}m{s}^{-2}$

Net acceleration = tangential acceleration + radial acceleration

$a_{net}=a_t+a_r$

$a_{net}=\frac{v}{t}+\frac{v^2}{r}$

$a_{net}=\frac{2t}{t}+\frac{2^2}{1}$

$a_{net}=2_t+4_r$

$|a_{net}|=\sqrt{4+16}=2\sqrt{5}$

Hence option B is correct