Question

A particle is projected vertically upwards with a velocity $u$ and from a point $O$ . When it returns to the point of projection, which of the following is incorrect ?

• A. average velocity is zero
• B. displacement is zero
• C. average speed is $u$
• D. average speed is $\frac{u}{2}$

Answer 1

Answer: (C)

Total displacement is $0$ as the particle returns to the original position, thus the average velocity is zero.
Total distance travelled is $2 \text{s}$ and total time taken is $2 \text{t}$
$0^{2} = \text{u}^{2} - 2 \text{gs}$

$\therefore $ $\text{s} = \frac{\text{u}^{2}}{2 \text{g}}$
Also $0 = \text{u} - \text{g} \text{ t}$
$\Rightarrow \text{t} = \text{u} / \text{g}$
$\therefore $ $2 \text{ t} = \frac{2 \text{u}}{\text{g}}$ $\text{ speed } = \frac{\text{u}^{2}}{\text{g}} / \frac{2 \text{u}}{\text{g}} = \frac{\text{u}}{2}$ ​.
Hence only option 3 has incorrect option and hence the option to be selected is 3.