course PHY201
Week 3 quiz 2Richard Hogan
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August 31, 2007
Determine the acceleration of an object whose velocity is initially 24cm/s and which accelerates uniformly through a distance of 66cm in 3.8 seconds.
Answer: With v0, ds, and dt given we can solve for acceleration(a) with the use of the following equation.
ds = v0(dt) + (1/2)(a)(dt^2) (Use distributive property)
ds = dt[v0 + (1/2)(a)(dt)] (Now divide both sides by dt)
ds/dt = v0 + (1/2)(a)(dt) (Now subtract both sides by v0)
(ds/dt) - v0 = (1/2)(a)(dt) (Now divide both sides by (1/2)(dt))
[(ds/dt) - v0] / (1/2)(dt) = a
[(66cm / 3.8s) - 24cm/s)] / (1/2)(3.8s) = a
-6.6cm/s / 1.9s = -3.5cm/s^2
a = -3.5cm/s^2
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Good solution.
Algebra was very good. Consider also the alternative approach, which is a little simpler:
Starting with `ds = v0(`dt) + (1/2)(a)(`dt^2) subtract v0 `dt from both sides the multiply both sides by 2 / (`dt)^2, then simplify.