(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The acceleration of point A is a = -5.4sin(kt) ft/s^{2}.

k = 3 rad/s.

When t = 0, x = 0 and v = 1.8 ft/s.

Determine the position and velocity of point A when t = 0.5s

Answers: x = 0.598 ft v = 0.1273 ft/s

2. Relevant equations

[URL]http://latex.codecogs.com/gif.latex?x=distance[/URL]

[URL]http://latex.codecogs.com/gif.latex?\dot{x}=velocity[/URL]

[URL]http://latex.codecogs.com/gif.latex?\ddot{x}=acceleration[/URL]

[PLAIN]http://latex.codecogs.com/gif.latex?\dot{x}(t_{2})=\dot{x}(t_{1})+\int_{t_{1}}^{t_{2}}\ddot{x}dt [Broken] [Broken]

[PLAIN]http://latex.codecogs.com/gif.latex?x(t_{2})=x(t_{1})+\int_{t_{1}}^{t_{2}}\dot{x}dt [Broken] [Broken]

3. The attempt at a solution

The velocity of point A at t = 0.5s is:

[PLAIN]http://latex.codecogs.com/gif.latex?\dot{x}(t_{2})=\dot{x}(t_{1})+\int_{t_{1}}^{t_{2}}\ddot{x}dt [Broken] [Broken]

[URL]http://latex.codecogs.com/gif.latex?\dot{x}(0.5)=1.8+\int_{0}^{0.5}[-5.4sin(kt)]dt=0.1273ft/s[/URL]

To find the position of point A at t = 0.5s, I want to use this formula

[PLAIN]http://latex.codecogs.com/gif.latex?x(t_{2})=x(t_{1})+\int_{t_{1}}^{t_{2}}\dot{x}dt [Broken] [Broken]

But, since I don't have a formula for [tex]\dot{x}[/tex], I'm not sure how to go about solving for the position of point A at time t = 0.5s.

So far, I have:

[URL]http://latex.codecogs.com/gif.latex?x(t_{2})=\int_{0}^{0.5}\dot{x}dt[/URL]

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# Homework Help: Find position and velocity at specific time

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