hi, here is a paraphased question i am having trouble with:

A vehicle's mass (including passenger) = 400 kg

after travelling 400 m the car stops accelerating. At this instant, the car's brakes are applied, and in addition, a small parachute opens at the rear to slow the car down.

The retarding force applied by the brakes including friction is 5000 N. The retarding force due to the parachute is 0.5v^2 N where v m/s is the velocity of the car x meters beyond the 400 m mark.

a) if a m/s^2 is the acceleration of the car during the retardation stage, write the equation of motion for the dragster during this stage:

now what i sorta got was this:

.5v^2 + 5000 = 400a

or (1/2)v^2 = 400a - 5000

is this right?

b) By choosing an appropriate derivative form for acceleration, show that the differential equation relating v to x is:

dv/dx = -(10^4 + v^2)/(800v)

Now, im thinking that there is a form for acceleration which goes:

d((1/2)v^2)/dx = a

which looks awfully similar to my (1/2v^2)

but im not too sure where to take it to show that equation.

Any help?