what is the relation between distance and time for constant power?
Answers
Answer:
In the above equation (3) the power and mass of the body is constant, so the distance covered by the body is proportional to the 3/2th power of time. Thus, the distance travelled by the body is proportional to t3/2
Answer:
The power of the body in the above problem is constant.
The formula to calculate the power of the body is given as,
P=F⋅v.(1)P=F⋅v.(1)
Here, P is the power of the body
F is the force on the body
v is the speed of the body
The velocity of the particle is given as,
v=stv=st
Here, s is the distance travelled by the body and t is the time in which the body covers the distance.
The force on the body is given as,
F=m⋅a.(2)F=m⋅a.(2)
Here, m is the mass of the body and a is the acceleration of the body.
The acceleration of the body is given as,
a=st2a=st2
Substitute st2st2for a in the equation (2) to find the force on the body.
F=m(st2)F=m(st2)
F=mst2F=mst2
Substitute mst2mst2for F and ststfor v in the equation (1) to find the power of the body.
P=(mst2)(st)P=(mst2)(st)
P=ms2t3P=ms2t3
s2=(Pm)t3s2=(Pm)t3
s=Pm−−−√(t3/2)(3)s=Pm(t3/2)..(3)