While running east west your speed was 20 ms your

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While running East-West, your speed was 2.0 m/s. Your total distance was 4.0 km, or 4000 m. Thus your total time running East-West was: t EW = 4 . 0 × 10 3 m 2 . 0 m/s = 2 . 0 × 10 3 s = 2 . 0 × 10 3 s 1 min 60 s = 33 min (2) This means that you ran North-South for 7 min, or 7 ? 60 = 420s. Your total North-South distance is therefore: d NS = 420 s × 3 . 0 m/s = 1260 m (3) (Notice that at this step I have kept too many significant figures). Half of this was going Northwards, so you traveled 1260/2 m = 630 m North. (b) What is your average speed in minutes per mile (a unit that many runners are fond of)? First, lets find your average speed in m/s. You ran East-West at a speed of 2.0 m/s for 33 minutes, and North-South at a speed of 3.0 m/s for 7 minutes. So your average speed was | ~v av | = 33 min × 2 . 0 m/s + 7 min × 3 . 0 m/s 40 min = 2 . 2 m/s (4) To convert this to minutes per mile, we first use a standard unit-conversion to change m/s to miles/minute: 2 . 2 m/s = 2 . 2 m/s × 1 mile 1600 m × 60 s 1 minute = 0 . 0825 miles/minute (5) Next, if I run 0.0825 miles in one minute, how many minutes does it take me to run one mile? This is equivalent to asking: 0 . 0825miles/minute × n minutes = 1 mile (6) i.e. n = 1 mile 0 . 0825 miles/minute = 12 minutes (7) Thus my average speed is 12 minutes/mile. 1
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2. The position of a yo-yo as a function of time is given by x ( t ) = A cos( pt + q ), where A = 0 . 60 m, p = 0 . 5 π s - 1 , and q = 0 . 5 π . (a) Sketch the Yo-yo’s position as a function of time, from t = 0 to t = 8 s. (Remember to feed the cosine an angle in radians!) Where is the velocity 0?
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