Question

The acceleration-time graph of a particle moving in a straight line is as shown in the figure. The velocity of the particle at time $\text{t}=0$ is $2\text{m/s}$. The velocity after $2$ seconds will be

• A. $2\text{m/s}$
• B. $6\text{m/s}$
• C. $4\text{m/s}$
• D. $8\text{m/s}$

Answer 1

The correct option is B $6\text{m/s}$

Area under $\text{a}-\text{t}$ graph gives the change in velocity $(\text{dv}=\text{adt})$.



Area under the curve
$=\frac{1}{2}\times \text{b}\times \text{h}$
Therefore,
${\upsilon }_f-{\upsilon }_i=\frac{1}{2}\times 2\times 4=4\text{m/s}$
Hence,
${\upsilon }_{\text{f}}={\upsilon }_i+4=2+4$
${\upsilon }_{\text{f}}=6m/s$

Final answer: (a).