Question

The potential energy (in joule) of a body of mass 2 kg moving in the x-y plane is given by
U = 6x + 8y
where the position coordinates x and y are measured in metre. If the body is at rest at point (6 m, 4m) at time t = 0, it will cross the y-axis at time t equal to

• A. 1 s
• B. 2 s
• C. 3 s
• D. 4 s

Answer 1

The correct option is B

2 s

Given that, U = 6x + 8y
Now, $F_x=\frac{-dU}{dx}=\frac{-d}{dx}(6x+8y)=-6N$
Therefore, the x component of acceleration is $a_x=\frac{F_x}{m}=\frac{-6}{2}=-3m{s}^{-2}$
The x coordinate of the body at time t is $x=x_0+\frac{1}{2}{a}_x{t}^2=6-\frac{1}{2}\times 3\times t^2=(6-\frac{3}{2}{t}^2)$
The body will cross the y-axis when x = 0, i.e. at time t given by $(6-\frac{3}{2}{t}^2)=0$ or t = 2 s.
Hence, the correct choice is (b).