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.