A time dependent force F =8 t acts on an object of mass 2 kg. If the object starts from rest, the work done by the force during the first 4 s will be J.

Question

A time dependent force F =8 t acts on an object of mass 2 kg. If the object starts from rest, the work done by the force during the first 4 s will be J. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

From Newton's second law, F =8 t = ma ∴ 2 a =8 t ∴ ( dv / dt )=4 t ∴ ∫ limits0 v dv =∫ limits04 4 t dt ∴ v =(2 t 2)04 ∴ v =32 m / s From work energy theorem, W F =Δ K . E .=(1/2) m ( v 2- u 2) =(1/2) 2(1024-0) ∴ W F =1024 J

Q. A time dependent force $F = 8 t$ acts on an object of mass $2 k g$ . If the object starts from rest, the work done by the force during the first $4 s$ will be __________ $J$ .

From Newton's second law,
$F = 8 t = ma$
$∴ 2 a = 8 t$
$∴ \frac{d v}{d t} = 4 t$
$∴ 0 \int v d v = 0 \int 4 4 t d t$
$∴ v = (2 t^{2})_{0}^{4}$
$∴ v = 32 m / s$
From work energy theorem,
$W_{F} = Δ K . E . = \frac{1}{2} m (v^{2} - u^{2})$
$= \frac{1}{2} 2 (1024 - 0)$
$∴ W_{F} = 1024 J$

Q. A time dependent force F=8t acts on an object of mass 2kg. If the object starts from rest, the work done by the force during the first 4s will be __________J.

From Newton's second law, F=8t=ma ∴2a=8t ∴dtdv​=4t ∴0∫v​dv=0∫4​4tdt ∴v=(2t2)04​ ∴v=32m/s From work energy theorem, WF​=ΔK.E.=21​m(v2−u2) =21​2(1024−0) ∴WF​=1024J

Q. A time dependent force $F = 8 t$ acts on an object of mass $2 k g$ . If the object starts from rest, the work done by the force during the first $4 s$ will be __________ $J$ .

From Newton's second law,
$F = 8 t = ma$
$∴ 2 a = 8 t$
$∴ \frac{d v}{d t} = 4 t$
$∴ 0 \int v d v = 0 \int 4 4 t d t$
$∴ v = (2 t^{2})_{0}^{4}$
$∴ v = 32 m / s$
From work energy theorem,
$W_{F} = Δ K . E . = \frac{1}{2} m (v^{2} - u^{2})$
$= \frac{1}{2} 2 (1024 - 0)$
$∴ W_{F} = 1024 J$