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It's Only a Minus Sign

Solve these differential equations to see how a minus sign can change the answer

Out in Space

Age 16 to 18
Challenge Level
Use the first part of the question to do the second part.

If you can separate the variables you can write the expression in the form $$\int f(x) dx = \int f(v) dv$$ and integrate to find the solution.

Take care over signs, acceleration is towards the Earth and displacement and velocity are measured in the opposite direction.