Question

A particle moves in circle of radius $9m$. Its linear speed is given by $v=3t$. What is the net acceleration of the partical at $T=2sec$.

• A. $3m/s^2$
• B. $4m/s^2$
• C. $5m/s^2$
• D. $6m/s^2$

Answer 1

The correct option is C $5m/s^2$

Given,

$r=9m$

$v=3t$

$t=2sec$

Linear speed, $v=3t=3\times 2=6m/s$

Radial acceleration at $t=2sec$

$a_r=\frac{v^2}{r}$

$a_r=\frac{6\times 6}{9}=4m/s^2$

Tangential acceleration, $a_t=\frac{dv}{dt}$

$a_t=3m/s^2$

The net acceleration of the particle at $t=2sec$,

$a=\sqrt{a_r^2+a_t^2}$

$a=\sqrt{4^2+3^2}=\sqrt{25}$

$a=5m/s^2$

The correct option is C.