Question

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

• A. $0.2\pi m/s$
• B. $2\pi m/s$
• C. $2m/s$
• D. zero

Answer 1

The correct option is C $2m/s$

V = 2t r = 20 cm = 0.2 m

Radial acceleration $=\frac{V^2}{r}$

$=\frac{4t^2}{0.2}=\frac{4\times 9}{0.2}\Rightarrow 180m/s^2$

tangential acceleration $=\frac{dy}{dt}$

$=\frac{d\left(2t\right)}{dt}$

$=2$

$at=2m/s$