Question

The acceleration vs distance graph for a particle moving with initial velocity $5 \,m / s$ is shown in the figure. The velocity of the particle at $x=35 \,m$ will be

• A. 20.62 m/s
• B. 20 m/s
• C. 25 m/s
• D. 50 m/s

Answer 1

Answer: (C)

Area of graph
$=\int a\, d x=\int \frac{v \,d v}{d x} \cdot d x==\int_{V_{i}} v\, d v $
$=\left[\frac{v^{2}}{2}\right]_{v_{i}}^{v_{t}}, 150+150=\frac{1}{2}\left[V_{f}^{2}-V_{i}^{2}\right] $
$300 \times 2=V_{f}^{2}-(5)^{2} $
$V_{f}^{2}=600+25, V_{f}=25$