# Calculus - another question

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"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 30km/h by increasing her speed steadily. How far did she travel in that ten minutes?"

I don't know how to begin this!

• Calculus - another question -

a = acceleration
v = Vi + a t
d = Xi + Vi t + (1/2) a t^2

30 = 0 + a t = 0 + a (10/60)
a = 30*60/10 = 180 km/hr^2

d = 0 + 0 + (1/2)(180)(10/60)^2
= 90/36
= 2.5 km

• Calculus - another question -

By the way the average speed was 30/2 = 15 for 1/6 of an hour
15/6= 2.5

• Calculus - another question -

Thank you! So the constants (Vi and Xi) are 0...why is that?

• Calculus - another question -

Xi is where you started, might as well be at the origin.
Vi is your speed at the start. Implied zero.

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