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# physics help?

Max paddles for 20 minutes on Pigeon Lake. For the first 10

minutes, he paddles at a rate of 4.0 m/s, then he takes a 4-

minute break. He finishes by paddling 5.5 m/s for the last 6

minutes.

a) Sketch Max’s position-time graph for his paddle. Label your graph

appropriately.

### 1 Answer

- 1 month ago
First, convert the speeds into meters/minute or convert the minutes to seconds

Convert minutes to seconds:

First 10 minutes => 600 seconds

4 minute break => 600 + 240 => 840 seconds

6 more minutes => 840 + 360 = 1200

From t = 0 to t = 600, he's paddling at 4 m/s

f(t) = 4t , 0 </= t </= 600

f(600) = 4 * 600 = 2400

From t = 600 to t = 840, he's resting

f(t) = 2400 , 600 </= t </= 840

From t = 840 to 1200, he's paddling at 5.5 m/s

f(t) = 2400 + 5.5 * t , 840 </= t </= 1200

So it's a piecewise function:

f(t) =

4t , 0 </= t </= 600

2400 , 600 </= t </= 840

5.5t + 2400 , 840 </= t </= 1200

</= is just my way of writing "less than or equal to" since I don't feel like learning alt-codes.

EDIT:

Converting m/s to meters/minute

4 m/s = 240 m/min

5.5 m/s = 330 m/min

f(t) = 240t , 0 </= t </= 10

f(t) = 2400 , 10 </= t </= 14

f(t) = 2400 + 330t , 14 </= t </= 20