A truck of mass 2000kg moving uphill @ 15ms requires force of 5000N to maintain constant speed.?

Question

What distance can it coast up hill if engine fails? What is slope of hill? If truck drives 200m down same hill under same force what is final speed?

Answer 1

Force down and parallel to the road that is pushing that truck is
F= W sin(A)
since it is under constant speed F=5000N
W=mg
Slope = F/W=F/mg=5000/(2000 x 9.8))
Slope =0.255
A= arcSin(0.255)=14.8 deg

The truck will negatively accelerate uphill and then accelerate down hill.


First what is its negative then positive acceleration (they are both the same in magnitude)

a= F/m= W sin(A)/m
a= mg (slope) /m
a= g (slope)

a=9.8 (0.255)=2.5 m/s

Uphill

vt=.5 at^2
v=.5 at
t=2v/a= 2 x 15 / 2.5=12 s

S=.5 a t^2= .5 x 2.5 (12)^2= 180m

Down hill
v=at
s= .5 a t^2
t=sqrt(2 s /a)
v=a sqrt(2 s /a)
v=sqrt(2 s a)
v=sqrt(2 x 200 x 2.5)=31.6 m/s

Answer 2

distance=v+u/2
=u=15/2
=7.5m