Question

The position x of a particle moving along x axis at time(t) is given by equation t=x^1/2+2,where x is un metres and t in seconds. Find the work done by force in first 4 seconds.
(1)Zero
(2)2
(3)4
(4)8
All are in Joules.

Answer 1

Answer on Question #49239-Physics-Mechanics-Kinematics-Dynamics

The position $x$ of a particle moving along $x$ axis at time $(t)$ is given by equation $t = x^{\frac{1}{2}} + 2$, where $x$ is un meters and $t$ in seconds. Find the work done by force in first 4 seconds.

(1) Zero

(2) 2

(3) 4

(4) 8

All are in Joules.

Solution

$$t = \sqrt {x} + 2 \rightarrow x = (t - 2) ^ {2}, x (0) = 2 ^ {2} = 4 m, x (4) = 2 ^ {2} = 4 m.$$

The work done by force in first 4 seconds is zero, because

$$W = \int_ {x (0)} ^ {x (4)} F x d x = \int_ {4} ^ {4} F x d x \equiv 0,$$

where $F$ is the force.

Answer: (1) Zero.

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