Question

Referring to a - x graph, find the velocity when the displacement of the particle is 100 m. assume initial velocity as zero.

• A. 9.8 m/s
• B. -10 $\sqrt{6}$ m/s
• C. 20 m/s
• D. 10 $\sqrt{6}$ m/s

Answer 1

The correct option is D

10 $\sqrt{6}$ m/s

Equation of line we get

(a-3) =$\frac{6-3}{150-50}+(x-50)$

a = $\frac{3}{100}x+\frac{3}{2}$

Now

a = v $\frac{dv}{dx}\Rightarrow v\frac{dv}{dx}=\frac{3}{100}x+\frac{2}{3}$

${\int }_0^{v}vdv={\int }_0^{100}(\frac{3}{100}x+\frac{3}{2})dx$

Limits are given in question itself

At x = 0 v = 0

At x = 100 m v = ?

After integrating

$\frac{v^2}{2}{]}_0^v=\frac{3x^2}{200}+\frac{3x}{2}{]}_0^{100}$

$\frac{v^2}{2}=\frac{300}{2}+\frac{300}{2}=300$

$v^2=600$

v = ± 10 $\sqrt{6}$

Since acceleration is increasing with x

So will the velocity.

So v = 10 $\sqrt{6}$ m/s