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 s = 5t2, where t is in seconds. Work
done by the force in 2 seconds is :-​

Answer 1

$\Huge\underline{\underline{\sf Answer}}$

$\large\underline{\underline{\sf Given:}}$

• Distance (s) = ⅓t²

• Time (t) = 2 sec

• Mass (m) = 3kg

$\large\underline{\underline{\sf To\:Find:}}$

• Work done by force (W) = ?

$\large\underline{\underline{\sf Solution:}}$

$\large{\boxed{\sf Work=F.ds }}$

Force (F) = ?

So ,

According to Newton's second law :

$\large{\boxed{\sf F=ma }}$

a = ?

$\sf{→s =\frac{1}{3}t^2}$

$\sf{→ v =2×\frac{1}{3}×t}$

$\sf{→ a = 2×\frac{1}{3}}$

${\sf →a=\frac{2}{3}m/s^2 }$

On putting value of a

$\large{\sf F = 3×\frac{2}{3} }$

$\large{\sf F=2N }$

On Putting value of Force :-

$\large{\boxed{\sf W=F.ds}}$

$\large{\sf →W=2×\frac{1}{3}×t^2 }$

$\large{\sf →W=2×\frac{4}{3}}$

$\large{\sf →W=\frac{8}{3}}$

Hence ,

$\red{\boxed{\sf Work\:done(W)=\frac{8}{3}J}}$

Answer 2

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

From the Question,

• Mass of the particle,m = 3 Kg

Displacement of the particle is defined as:

$\large{\sf{s = \frac{1}{3} t {}^{2}}}$

Differentiating s w.r.t to t,we get velocity of the particle:

$\large{\sf{v = \frac{ds}{dt} }} \\ \\ \rightarrow \ \sf{v = \frac{d( \frac{1}{3}t {}^{2} ) }{dt} } \\ \\ \rightarrow \: \huge{ \rm{v \: = \frac{2}{3}t \: ms {}^{ - 1} }}$

Differentiating v w.r.t to t,we get:

$\large{ \sf{a = \frac{dv}{dt}}} \\ \\ \rightarrow \ \sf{a = \frac{d(\frac{2}{3}t)}{dt}} \\ \\\huge{\rightarrow \: \boxed{\rm{a = \: {\frac{2}{3}} ms^{ - 2} }}}$

We Know that,

F = ma

→ F = ⅔(3)

→F = 2 N

When t = 2, displacement would be:

$\sf{s = \frac{1}{2} (2) {}^{2}} \\ \\ \huge{\implies \: \sf{s = \frac{4}{3}m}}$

$\therefore$

$\Huge{\boxed{\boxed{\sf{W = F.s}}}}$

Putting the values,we get:

$\sf{W = 2 \times \frac{4}{3} } \\ \\ \implies \ \huge{\sf{W = \frac{8}{3} J}}$

Thus,the work done by the force is 8/3 Joules

The correct option is____________(c)