"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!
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
By the way the average speed was 30/2 = 15 for 1/6 of an hour
15/6= 2.5
Thank you! So the constants (Vi and Xi) are 0...why is that?
Xi is where you started, might as well be at the origin.
Vi is your speed at the start. Implied zero.
To find out how far Margaret traveled in ten minutes, we need to start by understanding her cruising speed and the time it took her to reach that speed.
First, let's convert ten minutes into hours. There are 60 minutes in an hour, so 10 minutes is equal to 10/60 or 1/6 of an hour.
Now, we have to find out the distance Margaret traveled during this time. We can use the formula:
Distance = Speed * Time
Given that Margaret's cruising speed is 30 km/h, and the time is 1/6 of an hour, we can substitute these values into the formula:
Distance = 30 km/h * (1/6) hour
Multiplying 30 km/h by 1/6 of an hour gives us:
Distance = 30 km/h * (1/6) hour = 5 km
Therefore, Margaret traveled a distance of 5 kilometers in those ten minutes.