The velocity, v, of a moving body at time t is given by v = 50 - 10t. A) Find its acceleration. B) The initial displacement, s, is 40 meters. Find an expression for s in terms of t.
A) To find acceleration from a velocity equation, we must differentiate velocity, v = 50 - 10t.This gives us dv/dt = -10 = accelerationB) To find displacement from velocity, we must integrate the velocity equation, this will give us: s = 50t - 5t^2 +cAs displacement at t = 0 is 40 meters, we can substitute these values into the displacement equationThis gives us 40 = 50(0) - 5(0) +c, which shows that c =40.Therefore displacement, s, in terms of time, t, can be given by the equation: s = 50t - 5t^2 +40.
AS
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