need help and I also need help with making velocity Vs time graph for this quest

Question

need help and I also need help with making velocity Vs time graph for this question

Just for fun of it, you and a friend decide to enter the famous Tour de Minnesota bike race from Rochester to Duluth. You are riding along at the comfortable speed of 20 m.p.h. when you see in your mirror that your friend is going to pass you at what you estimate to be a constant 30 m.p.h. You will, of course, take up the challenge and accelerate just as she passes you until you pass her. If you accelerate 0.25 m.p.h. each second until you pass her, how long will she be ahead of you

Explanation / Answer

V1i=20mph=8.941m/s

V2i=30mph=13.41m/s

a=0.2mph/h = 0.0894m/s^2

Use below kinematic equations,

X=V1i*t+1/2*a*t^2 ---------------------(1) For me

X=V2i*t ------------------(2) For friends since here a=0m/s^2

From (1) and (2)

V1i*t+1/2*a*t^2 =V2i*t

8.941*t+1/2*0.089*t^2=13.4*t                      => t= 100s

V1f= V1i+a*t = 8.941+0.0894*100 = 17.881m/s = 40mph

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