Question

A particle is moving along a circle of radius $1\text{m}$ with an angular speed $\omega =2t^2+5$, the tangential acceleration of the particle after $2\text{seconds}$ is

• A. $2{\text{m/s}}^2$
• B. $4{\text{m/s}}^2$
• C. $8{\text{m/s}}^2$
• D. $13{\text{m/s}}^2$

Answer 1

The correct option is C $8{\text{m/s}}^2$

Given, radius of circular path $\left(r\right)=1\text{m}$ and
angular speed is given as , $\omega =2t^2+5$

Angular acceleration is the time rate of change of the angular velocity.

$\left(\alpha \right)=\frac{d\omega }{dt}=4t$
We know that tangential acceleration $\left(a_t\right)=r\alpha =1\times 4t=4\times 2=8{\text{m/s}}^2$

Hence option C is the correct answer