# Math Help - Another Motion Quesiton

1. ## 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

2. I suggest you use the equation of motion.

$V = Vi + at$
$30km/h = 8.333m/s$
$8.333m/s = 0 + a(10*60)$
$a = 0.014m/s^{2}$

Use the other equation of motion

$d =\frac{1}{2}at^{2}$
$d = \frac{1}{2}(0.014)(600)^{2}= 2500meters = 2.5 km$

3. 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.

4. Yeah we're not using distance equations like that though

5. Then follow the other suggest.

Use the fact that

Vi= 0
Vf = 30km/h

$a =\frac{dv}{dt}$

Then integrate the acceleration equation twice with respect to time to find the distance.

6. Alright sorry thank you both