drag racing

[hazakate]

i have a few formula for my physics assignment but i want to know the best way to set it out and what other formula i can use.

i already have the formula f=m*a and a=(v-u)/t.
i just really need the marks

[Chen]

Perhaps if you described what the assignment requires we would be of more help? You probably need a good grasp of mechanics, and that includes the formulas you list as well as some more. Here are just a few:

x(t) = x_0 + v_0t + \frac{1}{2}at^2
v(t) = v_0 + at
v = \frac{dx}{dt}
a = \frac{dv}{dt}
\Sigma F = ma

This might also be helpful:
http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#motcon

[ceptimus]

s = ut + 1/2 a t^2

For drag racing, u is zero. s is 1/4 mile (usually) (402.336 metres) so you get

402.336 = a/2 * t^2

t = sqrt(804.672 / a)

So you see that 1g (g = 9.81) acceleration will give you a 9 second run
or 5g would give a 4 second run

Real dragsters don't accelerate at a constant rate, but these formulae are ok as approximations.

[Chen]

You assume that the car accelerates not only constantly, but also throughout the race. Who's to say the car doesn't top at some value of V and proceeds with no acceleration at all?

[krab]

Usually, car is first traction-limited, in which case, applied force F is constant:
mdv/dt=F-Cv^2
At some point, it becomes power -limited with P constant:
mdv/dt=P/v-Cv^2
C is aerodynamic drag coefficient. Aero drag is much more important than rolling resistance, so I ignore a C_2v term.
BTW, you will notice that C can be derived from top speed v_\infty (where dv/dt=0):
C=P/v_\infty^3

[hazakate]

thank you this helps

[ray b]

You assume that the car accelerates not only constantly, but also throughout the race. Who's to say the car doesn't top at some value of V and proceeds with no acceleration at all?

when that happens you
A shift a gear
or if in top gear

B change final drive gears

but very few cars will do that in top gear
ie reach top speed in less than a 1/4 mile

[JohnDubYa]

ray b has it. If the car reaches maximum speed before it hits the traps, the mechanics will work the car over by changing the gears in the rear-end.