Question

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation $straight s equals 1 third straight t squared$ , where t is in s. Work done by the force in 2 s is:

$5 over 19 straight J$
$3 over 8 straight J$
$8 over 3 straight J$
$19 over 5 straight J$

Solution

8 over 3 straight J

If a constant force is applied on the object causing a displacement in it, then it is said that work has been done on the body to displace it.
Work done by the force = Force x Displacement
or W = F x s ...(i)
But from Newton's 2nd law, we have
Force = Mass x Acceleration
i.e., F = ma ...(ii)
Hence, from Eqs. (i) and (ii), we get
$straight W space equals space mas space equals space straight m open parentheses fraction numerator straight d squared straight s over denominator dt squared end fraction close parentheses straight s space space space space space space... left parenthesis iii right parenthesis space space space open parentheses because space straight a space equals space fraction numerator straight d squared straight s over denominator dt squared end fraction close parentheses Now comma space we space have comma space space straight s space equals space 1 third straight t squared therefore space space space space space space space space space fraction numerator straight d squared straight s over denominator dt squared end fraction space equals space straight d over dt open square brackets straight d over dt open parentheses 1 third straight t squared close parentheses close square brackets space space space space space space space space space space space space space space space space space space space equals straight d over dt cross times open parentheses 2 over 3 straight t close parentheses space space space space space space space space space space space space space space space space space space equals 2 over 3 dt over dt space space space space space space space space space space space space space space space space space space space space space space space space equals 2 over 3 space space space space space space space space space space space space space space space space space space space space space space$
Hence, Eq (ii) becomes
$straight W space equals 2 over 3 ms space equals space 2 over 3 straight m cross times 1 third straight t squared$
$equals 2 over 9 mt squared$
We have given
$straight m equals 3 space kg comma space straight t space equals space 2 straight s therefore space space space space straight w space equals space 2 over 9 cross times 3 cross times left parenthesis 2 right parenthesis squared space equals space 8 over 3 straight J$

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Motion In Straight Line

Some More Questions From Motion in Straight Line Chapter

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(d) Accelerated motion of a particle in a straight line.

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