Question

The displacement - time graph of a particle moving along a straight line is given below. Find its velocity at $t=1sec$.

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{2}{\sqrt{3}}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{3}{\sqrt{3}}$

Answer 1

The correct option is A $\frac{1}{\sqrt{3}}$

Given variation of x wrt t is following a circular path. Equaction of the circle passing through circle and centre at 5=2 is given by. $(t-2{)}^2+x^2=2^2$

So at $t=1sec,x=\sqrt{3}$

Differentiating wrt t we get $2(t-2)+2x\frac{dx}{dt}=0$

$\frac{dx}{dt}=\frac{-(t-2)}{x}$ putting value of x and t we get $v=\frac{dv}{dt}=\frac{1}{\sqrt{3}}.$

So best possible option is optionA.