HW#9 Ch 4: Motion in Two and Three Dimensions
Instructions: Write the general equation before showing your work to earn full credit.
1. A particle’s position coordinates (x, y) are (4m, −1m) at t = 0; (2m, 3m) at t = 3s; and (−3m, 7m) at t = 7s. a) Find vave from t = 0 to t = 3 s. b) Find vave from t = 0 to t = 7 s.
2. At t = 0, a particle located at the origin has a velocity of 25 m/s at θ = 45°. At t = 4s, the particle is at x = 40 m and y = 30 m with a velocity of 20 m/s at θ = 60°. Calculate a) the average velocity and b) the average acceleration of the particle during this interval.
3. A particle moves in an xy plane with constant acceleration. At time zero, the particle is at x = 4m, y = 3m, and has velocity \(\vec v = 2\frac{m}{s}\hat i - 9\frac{m}{s}\hat j\). The acceleration is given by the vector \(\vec a = 4\frac{m}{{{s^2}}}\hat i + 3\frac{m}{{{s^2}}}\hat j\). a) Find the velocity vector at t = 2s in unit vector notation. b) Find the position vector at t = 2 s in unit vector notation. c) Give the magnitude and direction of the position vector.
4. A particle has a position vector given by \(\vec r = \left( {30t} \right)\hat i + \left( {40t - 5{t^2}} \right)\hat j\), where r is in meters and t in seconds. Find the instantaneous velocity and instantaneous acceleration vectors as functions of time t.
5. A particle has a constant acceleration of \(\vec a = \left( {6\frac{m}{{{s^2}}}} \right)\hat i + \left( {4\frac{m}{{{s^2}}}} \right)\hat j\). At time t = 0, the velocity is zero and the position vector is \({\vec r_0} = \left( {10m} \right)\hat i\). a) Find the velocity vector and b) position vectors at any time t.