# Uniform acceleration

Classical Mechanics Level pending

A train accelerates uniformly from rest to a speed $$v$$ m/s. It continues at this speed for a period of time and then decelerates uniformly to rest. In travelling a total distance $$d$$ m the train accelerates through a distance $$pd$$ m and decelerates through a distance $$qd$$ m, where $$p < 1$$ and $$q < 1$$.

If the average speed of the train for the whole journey is $$\dfrac{v}{p+q+b}$$, find $$b$$.

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