Question

A watch a second hand 2 cm long. Calculate :i) the speed of the tip of the second handsii) the velocity of the tip at t=0 and t=15 seconds.iii) change in velocity from t=0 to t=15 seconds.

iv)- Average acceleration

Answer 1

Given:

$r=0.02\:\rm m$

$T=60\:\rm s$

(i) the speed of the tip of the second hand

$$v=\frac{2\pi r}{T}=\frac{2\pi*0.02}{60}=0.0021\:\rm m/s=2.1\: mm/s$$

ii) the velocity of the tip at  $t=0$

$$v_1=2.1\:\rm mm/s\quad to\: the\;right$$

and $t=15$ seconds

$$v_2=2.1\:\rm mm/s\quad downward$$

iii) change in velocity from $t=0$  to $t=15$  seconds

$$\Delta v=\sqrt{2}v=\sqrt{2}*2.1\:\rm mm/s=3.0\:\rm mm/s$$

iv) the average acceleration

$$a=\frac{\Delta v}{\Delta t}=\frac{3.0\:\rm mm/s}{15\:\rm s}=0.2\:\rm mm/s^2$$