Step 1: Write the equation for power
Power
(P) is force
(F) multiplied by velocity
(v) :
P=F⋅vStep 2: Replace force with mass and acceleration
Force is mass
(m) times acceleration
() :
P=m⋅vStep 3: Rearrange to separate variables
Move terms so you have all
v terms on one side and
t terms on the other:
v=Step 4: Integrate both sides
Integrate with respect to
v and
t :
∫vdv=∫dtAfter integrating:
=t Step 5: Solve for velocity
(v)v=√Step 6: Find the relationship between displacement and time
Velocity is the rate of change of displacement, so:
=√Step 7: Integrate to get displacement
(s)Integrate both sides with respect to
t :
∫ds=√∫t1∕2dtThe right side integrates to
t3∕2 :
s∝t3∕2Step 8: Answer
The value of
x is
.