A particle moves along the x axis. It is initially at the position 0.250 m, moving with velocity 0.090 m/s and acceleration -0.430 m/s2. Suppose it moves with constant acceleration for 5.80 s. (a) Find the position of the particle after this time. m (b) Find its velocity at the end of this time interval. m/s We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 5.80 s around the equilibrium position x= 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. (c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x. /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. m (e) Find its phase constant , if cosine rad used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need. (f) Find its position after it oscillates for 5.80 s. m (9) Find its velocity at the end of this 5.80 s time interval. m/s

A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Let's do a relativistic collision analysis to determine the mass and speed of the ball after the collision.

Given A = 5.00i + 4.00j, B = 3.00j – 7.00k. Find the vector C = 2A - B %3D %3D O + 4i – 10j – 7k O- 10j + 11k O 10i + 5j + 7k O + 8i + 7k O-7i - 8j + 14k 885 BBB 36 24 K

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