Question

The displacement 'x' (in metre) of a particle of mass 'm' ( in kg) moving in one dimension under the action of force, is related to time 't' ( in sec) by, t = √x+3. The displacement of the particle when its velocity is zero, will be

• A. 6 m
• B. 4 m
• C. 2 m
• D. 0

Answer 1

Answer: (D)

0

Answer 2

To find the displacement of the particle when its velocity is zero, we need to find the value of 'x' when the velocity is zero. Velocity is the derivative of displacement with respect to time.
Given:
t = (√x) + 3
Differentiating both sides with respect to 't':
1 = (1/2)(x)-1/2 * dx/dt
Since we want the velocity to be zero, the derivative dx/dt should be zero.
0 = (1/2)(x)-1/2 * dx/dt
Now we can solve for x:
0 = (x)-1/2
Taking the reciprocal of both sides:
0^(-1/2) = x
Since 0 raised to any negative power is undefined, we conclude that x must be zero.
Therefore, the displacement of the particle when its velocity is zero is 0 meters (option D).