Question

A particle moves in a circle of radius $20cm$. Its linear speed is given by $v=2t$, where $t$ is in second and $v$ is in $m/s$. Find the tangential acceleration at $T=3s$.

Answer 1

Step. 1 Given Data,

time, $t=3s$

$r=20cm$

Linear speed, $v=2t$

Step 2. Formula used,

Tangential acceleration,

$$a_t=r\times \frac{\text{d}\omega }{\text{d}t}$$

$$\frac{\text{d}\omega }{\text{d}t}$$= angular acceleration

$v=\omega r$, $v$ is the initial velocity, $\omega$is the angular velocity.

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

Step 3. Calculating the tangential acceleration,

The linear speed at $t=3s$ is $v=2t=6m/s$

$$\begin{gathered} a_t=\frac{dv}{dt} \\ {a}_t=2m/s^2 \end{gathered}$$

Hence, the tangential acceleration is $2m/s^2$.