exercise:94fac4cbea

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The position of a particle in motion in the plane is defined by the parametrization:

[[math]] P(t) = (x,y) = (t^2,t^3), \quad -2 \leq t \leq 2 . [[/math]]

• Draw the curve traced out by the particle during the interval [math][-2,2][/math].
• Compute the velocity vector [math]\vec v(t)[/math]. Find the position, velocity, and speed at [math]t=-2[/math], [math]t=0[/math], [math]t=1[/math], and [math]t=2[/math]. Indicate these positions and draw the velocity vectors in the figure in (a).
• Compute the accleration vector [math]\vec a(t)[/math]. Determine the four specific vectors [math]\vec a(-2)[/math], [math]\vec a(0)[/math], [math]\vec a(1)[/math], and [math]\vec a(2)[/math], and draw them in the figure in (a).