Question

A particle is moving in a circle of radius $4cm$ with constant speed of $1cm/s$. Sum of average speed, average velocity and average acceleration in a time interval from $t=0$ to $t=\frac{T}{4}$ be $x$. Here, $T$ is the time period of the particle. Find $x$.

Answer 1

At $t=0$, $a_c=\frac{v^2}{r}=\frac{1^2}{4}=0.25\hat{y}cm/s^2$

Also $v=1\hat{x}cm/s$

At $t=\frac{T}{4}$, $a_c=\frac{v^2}{r}=\frac{1^2}{4}=-0.25\hat{x}cm/s^2$

Also $v=1\hat{y}cm/s$

Thus average acceleration $a_{avg}=\sqrt{2}\left(0.25\right)=0.3535cm/s^2$

Average velocity $v_{avg}=\sqrt{2}\left(1\right)=1.414cm/s$

Average speed $s_{avg}=1cm/s$

$x=0.3535+1.414+1=2.77$

$\left[x\right]=2$