A force given by the relation F=8t, acts on a body of mass 2kg , initially at rest. Find the work done by this force on the body during first 2 seconds of its motion.

Question

A force given by the relation F=8t, acts on a body of mass 2kg , initially at rest. Find the work done by this force on the body during first 2 seconds of its motion. (A) 64J (B) zero (C) -64J (D) none of these

Tardigrade Admin · Accepted Answer

F=ma=8t a=8t (d v/d t)=8t dv=8tdt displaystyle ∫ 0vdv= displaystyle ∫ 8tdt (8 t2/2)=|4 t2|02 V=16ms- 1 w=Δ K =(1/2)× (.2.)((16)2 - 0) =64J

Q. A force given by the relation $F = 8 t,$ acts on a body of mass $2 k g$ , initially at rest. Find the work done by this force on the body during first $2$ seconds of its motion.

$64 J$

zero

$- 64 J$

none of these

$F = ma = 8 t$
$a = 8 t$
$\frac{d v}{d t} = 8 t$
$d v = 8 t d t$
$\int_{0}^{v} d v = \int 8 t d t$
$\frac{8 t ^{2}}{2} = ∣ ∣ 4 t^{2} ∣ ∣_{0}^{2}$
$V = 16 m s^{- 1}$
$w = Δ K$
$= \frac{1}{2} \times (2) ((16)^{2} - 0)$
$= 64 J$

Q. A force given by the relation F=8t, acts on a body of mass 2kg , initially at rest. Find the work done by this force on the body during first 2 seconds of its motion.

64J