Question

<Homework Section 2: Motion in One Dimension Motion with Non-constant Acceleration I A cheetah has an acceleration as a function of time given by a(t)=-(0.400)t Part A Initially the cheetah is moving with a speed of 10.0 m/s to the right Write an expression which gives the cheetah's velocity as a function of time Do not include units in any numerical values in your expression VA X.10

please help work out all three parts

Answer 1

a = -0.400 t^2 A) v(t) = integral a dt = -0.400/3 t^3 + c At t = 0, v = 10 m/s implies c = 10 Therefore v(t) = -0.400/3 t^3 + 10 B) x(t) = integral v(t) dt = -0.400/3 times 4 t^4 + c = -t^4/30 + c At t = 0, x(0) = 4, implies c = 4 implies x(t) = -t^4/30 + 4 \r\n C) when v = -10 m/s Therefore -10 = -0.4/3 t^3 + 10 therefore 0.4 t^3 = 60 implies t = [600/4]^1/3 = (150)^1/3 Therefore x(t) = x((150)^1/3) = -(150)^4/3/30 + 4 = -22.566 m
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