Question

A particle moves along a straight line with acceleration a = (2 - 3s), where the unit for a is m/s^2 and s is m. Write down the relationship between the velocity with the displacement of the particle if given s = 4 m ,the velocity of the particle v = 2m/s?

Answer 1

$a = 2 - 3s \\ \frac{dv}{ds} = 2 - 3s \\ dv = (2 - 3s)ds \\ integrate \\ v = 2s - \frac{3}{2} {s}^{2} + c \\ when \: s = 4 \: \: then \: v = 2 \: \\ so \: put \: here \\ 2 = 2(4) - \frac{3}{2} (16) + c \\ 2 = 8 - 24 + c \\ c = 18 \\ eqn \: becomes \: \\ v - 2s + \frac{3}{2} {s}^{2} = 18$


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