# Newton's Second Law ODE Question

A car of mass 1200 kg is started from rest and pulled on the level ground by an engine. The resistance of the motion is Kv, where v(m/s) is the velocity of the car at time t(s). The power of the engine is constant and equal to 80000 watts.

a) How does P, the power of the engine connect to F, the Driving Force?
b) By Newton's Second Law of Motions, write down the Differential Equation which describes the Motion.
c)State the condition for the maximum velocity to occur in this motion.
d) If the maximum velocity of the motion is 144km/h, find the value of k.
e)Solve the Differential Equation for x in terms of v.
f) Draw a graph of x against v.
g)State 2 characteristics of the graph.
h) Hence find the distance which a velocity of 15m/s can be reached from rest.

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Could anyone help me solve this problem? It has been mind-boggling for me cause I have only started to venture into this topic.

HallsofIvy
Homework Helper
It is apparent that this is your first post here and that you did not read the "rules" that you had to say you had read when you registered. You have done just about everything wrong.

The way this is written makes it obvious that it is a homework problem. I am moving it to the homework section. And you must show what effort you have made yourself before you will be given any help. Finally you have "bumped" after only 52 minutes! Continuing to do any of those things can get you banned.

Ah... Okay. Sorry. Thanks. Is there a place I can go to ask such questions? And I'm not sure how to continue as I'm already lost from the beginning cause I don't know what is the concept behind it. In any case, I apologize for my tardiness.

This is now in the right place. But you still need to show what YOU have done on this problem and what prevents you from going further.

a) R = kv
Summation F = F-R
= F - kv
By Newton's Second Law of F=ma,
F - kv = ma
F = ma+kv
= m(dv/dt) + kv
Thus, P=FV.
b) ODE = P=FV
=(m(dv/dt) + kv)(v)
=mv(dv/dt)kv^2
c)V = Vmax when a=0
Thus summation F= 0
F-kv=0
F=kv
d) Given P = 80000Watts, V = 40m/s
Since P=FV,
=(kv)v
=kv^2
k=P/V^2
=80000/(40^2)
=50

I'm lost after this step. Sorry for any inconvenience caused.