Question

A body of mass 3 kg is under the the force, which causes displacement in it is given by S=t^3/3 (in m). Find the work done by the force in first 2 sec.
(1)2
(2)3.8
(3)5.2
(4)24
All are in joules

Answer 1

Answer on Question #50063, Physics, Mechanics | Kinematics | Dynamics

Task:

A body of mass $3\mathrm{kg}$ is under the force, which causes displacement in it is given by $S = t^3 / 3$ (in m). Find the work done by the force in first 2 sec.

(1)2

(2)3.8

(3)5.2

(4)24

All are in joules

Solution:

$$v = d S / d t = t ^ {2}$$ $$v _ {0} = v (t = 0) = 0 m / s$$ $$v _ {f} = v (t = 2 s) = 4 m / s$$ $$K E _ {o} = \left(^ {1} / _ {2}\right) m v _ {o} ^ {2} = \left(^ {1} / _ {2}\right) (3. 0 k g) (0 m / s) ^ {2} = 0 J$$ $$K E _ {f} = \left(^ {1} / _ {2}\right) m v _ {v} ^ {2} = \left(^ {1} / _ {2}\right) (3. 0 k g) (4 m / s) ^ {2} = 2 4 J$$ $$W _ {n e t} = \triangle K E = 2 4 J$$

Answer: (4)24

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