Question

The position of a particle is given by the following equations: x = at + bt^3 where a = 2.0 m/s and b = 0.5 m/s^3. y = Asin(Bt) where A = 2.0 m and B = 2 rad/s. a) Write equations for the components of the velocity, vx and vy, as functions of time. b) Write equations for the components of the acceleration, ax and ay, as functions of time. c) Make an XY plot showing (as dots numbered 0 and 1) the position of the particle at t = 0 and 1 seconds. On this same plot, draw two arrows at each dot showing the approximate direction of the velocity and acceleration at that time. If either velocity or acceleration has zero magnitude, indicate that clearly. Label your two arrows so we know which is which. Don't worry about the length of these arrows, just their approximate directions.

          The position of a particle is given by the following equations: x = at + bt^3 where a = 2.0 m/s and b = 0.5 m/s^3. 
y = Asin(Bt) where A = 2.0 m and B = 2 rad/s.

a) Write equations for the components of the velocity, vx and vy, as functions of time.
b) Write equations for the components of the acceleration, ax and ay, as functions of time.
c) Make an XY plot showing (as dots numbered 0 and 1) the position of the particle at t = 0 and 1 seconds. On this same plot, draw two arrows at each dot showing the approximate direction of the velocity and acceleration at that time. If either velocity or acceleration has zero magnitude, indicate that clearly. Label your two arrows so we know which is which. Don't worry about the length of these arrows, just their approximate directions.

Added by Esther W.

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