
Another Motion Quesiton
Margaret has found that by a proper choice of gears she can steadily increase her speed on her bike. One day she sets out and, ten minutes later, she achieves her cruising speed of 30 km/h by increasing steadily. How far did she travel in this time?
No idea where to begin

I suggest you use the equation of motion.
$\displaystyle V = Vi + at $
$\displaystyle 30km/h = 8.333m/s $
$\displaystyle 8.333m/s = 0 + a(10*60) $
$\displaystyle a = 0.014m/s^{2} $
Use the other equation of motion
$\displaystyle d =\frac{1}{2}at^{2}$
$\displaystyle d = \frac{1}{2}(0.014)(600)^{2}= 2500meters = 2.5 km $

If your acceleration is constant, just use rise/run from (0,0) to (10,30) to calculate it. Then you can just use a distance equation for your first integral of 3/2x^2. Not really a calc question.

Yeah we're not using distance equations like that though

Then follow the other suggest.
Use the fact that
Vi= 0
Vf = 30km/h
$\displaystyle a =\frac{dv}{dt}$
Then integrate the acceleration equation twice with respect to time to find the distance.

Alright sorry thank you both