Question

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

• A. $2.47cm{s}^{-2}$
• B. $3.47cm{s}^{-2}$
• C. $4.47cm{s}^{-2}$
• D. $5.47cm{s}^{-2}$

Answer 1

The correct option is C $4.47cm{s}^{-2}$

v=2 cm/s , r=1 cm

Here, radial acceleration at 1 sec will be

$a=(\frac{v^2}{r}$)= $4cm{s}^{-2}$

Tangential acceleration at 1 sec will be

$a=\frac{dv}{dt}$

=$2cm/s^2$

Magnitude of acceleration at 1 sec is

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

=$\sqrt{20}cm/s^2$