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**Hi Folks: I am puzzled by this problem; there must be something wrong but I can't see what...**

1. The problem statement: "A runner enters the last 200 m of a race running 6 m/s. She accelerates at 0.2 m/s2 &crosses the finish line at 10 m/s. What is her time for the last 200 m?"

2. Homework Equations : "

1. The problem statement: "A runner enters the last 200 m of a race running 6 m/s. She accelerates at 0.2 m/s2 &crosses the finish line at 10 m/s. What is her time for the last 200 m?"

2. Homework Equations : "

**(HINT: use V-V0=a*t to find time. Then use X = Vo*t + 0.5*a*t^2 to get t)."**## The Attempt at a Solution

:**V-V0=a*t --> 10-6=0.2*t --> 4=0.2*t --> t=4÷0.2=20s.**

That self-checks:

That self-checks:

**V-V0=a*t --> V-6=0.2*20 --> V=4+6=10m/s**

But the second part is more problematic. X is the distance; I plug in the 20s from the first equation.But the second part is more problematic. X is the distance; I plug in the 20s from the first equation.

X = Vo*t + 0.5*a*t^2[/B]

**X = 6*20 +0.5*0.2*(20^2)**

X = 120+0.01*400 = 120+40 = 160...instead of 200 as it should be!

It's also possible to put X=200 from the problem, and solve a quadratic for t, but that is a big pain in the rear. Anyway, I am really wondering what silly step I am missing that part 2 gives me 160 instead of 200??!

X = 120+0.01*400 = 120+40 = 160...instead of 200 as it should be!

It's also possible to put X=200 from the problem, and solve a quadratic for t, but that is a big pain in the rear. Anyway, I am really wondering what silly step I am missing that part 2 gives me 160 instead of 200??!