Question

A particle moves in a circle of radius $2.0cm$ at a speed given by $v=4t$, where $v$ is in cm/s and $t$ is in seconds. Find total acceleration at $t=1s$.

• A. $4\sqrt{5}cm/s^2$
• B. $2\sqrt{5}cm/s^2$
• C. $4\sqrt{3}cm/s^2$
• D. $4cm/s^2$

Answer 1

The correct option is A $4\sqrt{5}cm/s^2$

Answer is A.

Tangential acceleration, $a_t$ = $\frac{dv}{dt}$= 4 cm/s${}^2$

Centripetal acceleration, $a_c=\frac{v^2}{R}=\frac{(4{)}^2}{2}=8cm/s^2\Rightarrow a=\sqrt{a_t^2+a_c^2}=\sqrt{(4{)}^2+(8{)}^2}=4\sqrt{5}cm/s^2$.

Hence, total acceleration at t = 1s is $4\sqrt{5}cm/s^2$.