Question

The velocity-time graph of a particle moving along a straight line is as shown in the diagram. The rate of acceleration and retardation is constant and is equal to $\text{5}{\text{m s}}^{-2}$ . If the average velocity during the motion is $\text{20}{\text{m s}}^{-1},$ then the maximum velocity of the particle is

• A. $\text{20}{\text{m s}}^{-1}$
• B. $\text{25}{\text{m s}}^{-1}$
• C. $\text{30}{\text{m s}}^{-1}$
• D. $\text{40}{\text{m s}}^{-1}$

Answer 1

Answer: (B)

Average speed $=20{\text{m s}}^{-1}$
$\frac{\text{Total distance}}{\text{Total time}}=20\Rightarrow \frac{\text{Area of graph}}{20+\text{t}}=20$
$\Rightarrow \frac{1}{2}\left(20+\text{t}+20-\text{t}\right)\times 5\text{t}=20\left(20+\text{t}\right)\Rightarrow \text{t}=5\text{ s}$ Maximum velocity $=5t=5\times 5=25{\text{m s}}^{-1}$