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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.