Question

The displacement - time graph of a particle at time $t$ makes angle $45^{\circ}$ with the time axis. After two seconds, it makes an angle $60^{\circ}$ with the time axis. What is the average acceleration of the particle?

• A. $\frac{1}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{(\sqrt{3}-1)}{2}$
• D. $\frac{(\sqrt{3}+1)}{2}$

Answer 1

Answer: (C)

Initial velocity, $u=\tan 45^{\circ}=1$
Velocity after $2 s , v=\tan 60^{\circ}=\sqrt{3}$
$\therefore $ Average acceleration, $a_{ av }=\frac{v-u}{t}=\frac{\sqrt{3}-1}{2}$