Answer:
Check Explanation.
Explanation:
At rest, the car had zero kinetic energy, that is K(rest) = 0. The kinetic energy of the car when the car moved, k(moved) can be calculated by using the work- energy relationship that is;
Work, W= k(moved) - k(rest).
k(moved) = work, W + k(rest).
[Recall that k(rest) = 0]. Therefore, k(moved) = work, W.
{Two Important equations to note are (1). Work, W=( 1/2) mass,m × (speed, V)^2 and (2). Power, P = work,W/ time,t}.
Hence, k(moved) = ( 1/2) mass,m × (speed, V)^2 ---------------------------(1).
Since, power, P= W/t -----------------(2).
Then, equation (2) becomes;
Power, P = m × v^2/ 2 × t.
Making, speed, v the subject of the formula, we have;
v = [(2 × P × t)/ m]^ 1/2. ---------------(3).
Another thing we have to remember is the formula for speed which is the change in distance with time that is; ds/ dt.
Therefore, ds/ dt = [(2 × P × t)/ m]^ 1/2.
ds/dt = [(2 × P)/ m]^ 1/2 × t^ 1/2 ------(4).
Then, the integration of the equation (4) above will give us;
s = ( 8P 9m )^ 1/2 × t^ 3/2 .
(Check attachment for more).
Answer:
Please look in the explanation section
Explanation:
Using the equation of kinetic energy:
[tex]E_{k} =\frac{1}{2} mv^{2}[/tex]
Where
m is the mass, v is the velocity. The equation of power is:
[tex]P=\frac{W}{t}[/tex]
Where W is the work and t is the time. Initially, the work is equal to the kinetic energy:
[tex]W=E_{k-initial} \\P=\frac{E_{k-initial}}{t} \\P=\frac{mv^{2} }{2t}[/tex]
Clearing v:
[tex]v=\sqrt{\frac{2tP}{m} }[/tex]
The velocity is:
[tex]v=\frac{ds}{dt}[/tex]
Replacing:
[tex]\frac{ds}{dt} =\sqrt{\frac{2tP}{m} }\\ds=\sqrt{\frac{2tP}{m} }dt[/tex]
Integrating:
[tex]s=\sqrt{\frac{2P}{m} } (\frac{2t^{3/2} }{3} )=\sqrt{\frac{8P}{9m} } t^{3/2}[/tex]
