kinematic word problem with two objects

Question

Ryan and Eddie ran in the same direction at t=0. Ryan ran with an average velocity of 10 m/s while Eddie slowly increased his speed to 8 m/s in 20 seconds, then maintained its final velocity for the rest of the run. How far are they from each other after 2 minutes?

Answer 1

x_R = vt = 10t (note that this should be a constant velocity, not an average)

x_E = ((8 +0)/2)20 + 8(t-20) where the first term is v_avg(20s)*20s and the next term is the constant velocity of 8m/s starting at t=20.

Since we are interested in a time of 2 minutes, we know the 2nd equation is correct (the time is past the ramp up part). It is now just a matter of subtracting the values at t = 120 s:

x_R-x_E = 10t - (80 + 8(t-20)) for t = 200

You could also divide the problem into 2: t<20 and t>20 (1st part will be 10(20)-80 and second part will be (10-8)*(120-20)

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