Mechanics, help! (1 Viewer)

[fahadmumtaz88]

A particle of mass 4kg moves from rest under the action of a force whose magnitude after t seconds is 6-2t kg wt. When the particle reaches a speed of 19.6 m/s, the force ceases and the particle continues at constant speed for 5s, and is then brought to rest by a constant force of 5kg wt. Calculate the total distance travelled.

Can someone plz help out wif this question. Any suggestion will be appreciated. BTW dis question's from New Senior Mathematics Exercise 35(a) question 1, and the question following it, i.e. question 2, seems to have wrong answer at da back, im definite that da answer shud be -48m/s, instead at the back it say -486, dunnoo why?

PLZ help.

Thanx

 

[martin]

basically use F=ma
so a=F/m=(6-2t)/4=3/2-t/2

You should then be able to integrate up to find v=int(a)dt and x=int(v)dt putting in the appropriate constants so that v(0)=0 and x(0)=0.

Then put v=19.6 to find the time, t_max, when it reaches this speed, then x(t_max) is the distance in the first part, 5*19.6 is distance when there is no force on it.

After this start again with F=-5 v(0)=19.6, x(0)=x(t_max)+5*19.6, then find t_stop so that v(t_stop)=0 then x(t_stop) is your total distance.

I haven't actually done this, but does that description help?

 

[martin]

I think that there's another little trick in this question, the force is only positive for the first three seconds so the particle is going to turn around.

a=3/2-t/2
v=(3/2)t-(1/4)t^2
x=(3/4)t^2-(1/12)t^3

The particle is going its fastest in the positive direction at t=3 (before force becomes negative) but v(3)=9/2-9/4=9/4 < 19.6.

So I think you'll have to put v=-19.6 (question said speed was 19.6 not velocity so it could be either plus or minus). Also need to include the distance travelled in the positive direction. x(3)=27/4-27/12=9/2 so need to add 2*9/2=9 to total (going back and forth).

Also in last bit need F=5 (not -5) so that its acting in the right direction. Draw yourself a picture.

 

[noah]

this is out of the fitzpatrick book and they use stupid units for force in a couple of their questions. kg wt or kilograms weight is a gravitational unit of force. 1 kg wt is the force on one kilogram at the earths surface. therefore to conver kg wt into newtons times them by 9.8.