Question

A body is acted upon by a force of 10 N and undergoes a displacement in the direction of the force in accordance with the relation s = 3t² + 2t, where s is the displacement in meters and t is in seconds. The rate at which the force is doing work at the instant t = 2s is...

A) 14 W
B) 160 W
C) 120 W
D) 140 W
E) 12 W

Answer 1

put t =2 in
s=3(2)^2+2*2
s=16
now
w=Fd cos 0 because force and displacement in same direction

Answer 2

W=10*16
W=160

Answer 3

It's funny because unit is watt, so I think I was supposed to find power or something.

W = 160 J...

Answer 4

power is the rate at which work is done meaning it the workdone per time unit. one watt =1joule/second. work done=160j/s therefore power =160w

Answer 5

Why can't I use \(\int\limits \!\! \int\limits F \text{ d}\! s \text{ d}\! t \) where \(W = \int\limits F \text{ d}\! s\)

Answer 6

There is no way around the fact that we have calculated the work done after 2 seconds as 160J. This is NOT the current power output.

I think you need to differentiate the function, s(t) = 3t² + 2t to get the rate of displacement. This can give you the rate of work done (i.e. power). I.e\[Power = \frac{ W }{ dt } = F \frac{ s(t) }{ dt }\]
The answer I get is one of the options..

Answer 7

So... the answer is 140 W? This is what I got.

Answer 8

@furnessj

Answer 9

@mayankdevnani @mahmit2012

Answer 10

answer is 160W

Answer 11

s = 3t² + 2t,
t =2 in ___
s=3(2)^2+2*2

Answer 12

ok @geerky42

Answer 13

s=16

Answer 14

Work done=Force*Displacemnt
W=F*s
W=10N*16m
W=160Nm=160J

Answer 15

you find that The rate at which the force is doing work at the instant t = 2s is...
so it is POWER. at any instant convert J(Joule) into W(Watt) because question says at instant

Answer 16

ok @geerky42

Answer 17

I see. Thanks.

Answer 18

welcome

Answer 19

I disagree with you mayankdevani, the units are simply not dimensinally correct for power using force x distance moved. Power is also defined as F x velocity, and ds/dt is the velocity...
http://hyperphysics.phy-astr.gsu.edu/hbase/pow.html

Answer 20

@furnessj has good point. Can you defend yourself and explain and why you think your answer is correct? @mayankdevnani