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 $t=0\, s$. The velocity at time $t=15\, s \left(v_{15}\right)$ and at $25\, s$ $\left(V_{25}\right)$, 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 $t=15\, s$
$v_{15}=$ Area of $(\Delta O A E+A B D E)$
$=\frac{1}{2} \times 10 \times 10+10 \times(15-10)=100\,m / s$
Similarly, velocity at time $t=25\, s$
$v_{25} =$Area of $(\Delta O A E+A B D E+\Delta B C D) $
$=\frac{1}{2} \times 10 \times 10+10 \times(15-10)+\frac{1}{2} \times 10 \times(25-15)$
$=150\,m / s$