Question

A particle moves in a circle of radius $30cm$. Its linear speed is given by: $V=2t$, where $t$ in second and $v$ in $m/s$. Find out its radial and tangential acceleration at $t=3\sec$ respectively.

• A. $220m/{\sec }^2,50m/{\sec }^2$
• B. $110m/{\sec }^2,5m/{\sec }^2$
• C. $120m/{\sec }^2,2m/{\sec }^2$
• D. $110m/{\sec }^2,10m/{\sec }^2$

Answer 1

Answer: (C)

Given : $r=30cm=0.3cm=0.3m$ and $V=2t$
Radial acceleration at $t=3\sec$
$a_r=\frac{v^2}{r}=\frac{4t^2}{0.3}=\frac{4\times (3{)}^2}{0.3}=120m/s^2$
and tangential acceleration
$a_t=\frac{dv}{dt}=2m/s^2$