Question

The following plot gives the variation of acceleration $\left(m/s^2\right)$ with time (s) for an object that started from rest at time $t=0s$. The velocity at time $t=15s\left(v_{15}\right)$ and at $25s$ $\left(V_{25}\right)$, respectively are

• A. $V_{15}=50$ m/s and $V_{25}=0$ m/s
• B. $V_{15}=100$ m/s and $V_{25}=150$ m/s
• C. $V_{I5}=50$ m/s and $V_{25}=25$ m/s
• D. $V_{I5}=100$ m/s and $V_{25}=25$ m/s
• E. $V_{I5}=75$ m/s and $V_{25}=50$ m/s

Answer 1

Answer: (B)

As, we know that, area of acceleration-time (a-t) graph gives the velocity. A plot of variation of acceleration with time is given below

The velocity at time $t=15s$
$v_{15}=$ Area of $(\Delta OAE+ABDE)$
$=\frac{1}{2}\times 10\times 10+10\times (15-10)=100m/s$
Similarly, velocity at time $t=25s$
$v_{25}=$Area of $(\Delta OAE+ABDE+\Delta BCD)$
$=\frac{1}{2}\times 10\times 10+10\times (15-10)+\frac{1}{2}\times 10\times (25-15)$
$=150m/s$