This is a mechanics question but since it requires calculus to solve it, I am posting it here.

\(\displaystyle v=k(200t-t^2)\)

Where

Distance= 200m

Time= 100s

\(\displaystyle ds/dt=k(200t-t^2)\)

\(\displaystyle \int{ds}=\int{k(200t-t^2)dt}\)

\(\displaystyle s=k(\frac{200t^2}{2}-\frac{t^3}{3})+c\)

Have I done the above 3 steps correctly?

\(\displaystyle v=k(200t-t^2)\)

Where

Distance= 200m

Time= 100s

**My Attempt**\(\displaystyle ds/dt=k(200t-t^2)\)

\(\displaystyle \int{ds}=\int{k(200t-t^2)dt}\)

\(\displaystyle s=k(\frac{200t^2}{2}-\frac{t^3}{3})+c\)

Have I done the above 3 steps correctly?

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