A puck is moving on an air hockey table. Relative to an x, y, coordinate system

Question

A puck is moving on an air hockey table. Relative to an x, y, coordinate system at time t = 0 s, the x component of the puck's initial velocity and acceleration are v0x = +1.0 m/s and ax = +1.9 m/s2. The y components of the initial velocity and acceleration are v0y = +2.0 m/s and ay = -1.2 m/s2.
(a) Is the magnitude of the x component of the velocity increasing or decreasing in time?
---Select--- increasing decreasing
(b) Is the magnitude of the y component of the velocity increasing or decreasing in time?
---Select--- increasing decreasing
(c) Find the magnitude and direction of the puck's velocity at a time t = 0.60 s. Specify the direction relative to the +x axis. Be sure that your calculations are consistent with your answers above.
m/s
° ---Select--- above below the +x axis

Explanation / Answer

Given that the components of initial vlocity is v_0x = + 1.0 m/s , v_0y = + 2.0 m/s acceleration is a_x = 1.9 m/s^2 , a_y = - 1.2 m/s^2 a ) velocity of the x component is v_x = v_0x + a t                                                            = ( + 1.0 m/s) + ( 1.9 m/s^2 ) ( 0.6 s)                                                            = 2.14 m/s b ) The magnitude of the y component is v_y = v_0y + a_y t                                                                         = 2.0 m/s + ( - 1.2 m/s^2 ( 0.6 s)                                                                         = 1.28 m/s c )  the magnitude and direction of the puck's velocity at a time t = 0.60 s is            v = v_x^2 + v_y^2                = ( 2.14 m/s)^2 + ( 1.28 m/s)^2                = 2.49 m/s direction is = tan^-1 ( v_y / v_x)                         = tan^-1 ( 1.28 / 2.14)                        = 30.8 degrees above positive x - axis

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