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Assume that the net force is constant and is given by <0, -5 N>. An object with a mass,

2.0 kg, is initially at origin and is subjected to this force. The object has a velocity of
<3.6 m/s, 4.8 m/s> at time zero. Use your mathematical procedure to determine the
motion of the object over the next 4 seconds. To determine the motion of the object, you
may determine its x and y positions at various times and plot graphs of x vs. time and y
vs. time. The path of the object can be determined by plotting y vs. x. What can you
conclude about the motion of the object?

User Sargupta
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1 Answer

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Final answer:

To determine the motion of the object subjected to a constant force, we calculate acceleration using Newton's second law, then apply kinematic equations for the y-direction with constant speed maintained in the x-direction, resulting in parabolic motion.

Step-by-step explanation:

To determine the motion of an object with a constant net force of <0, -5 N> acting on a 2.0 kg mass that starts from the origin with an initial velocity of <3.6 m/s, 4.8 m/s>, we can employ Newton's second law and kinematic equations. First, we calculate the acceleration in the y-direction as a_y = F_y / m, where F_y is the force in the y-direction and m is the mass of the object. In this case, a_y = -5 N / 2.0 kg = -2.5 m/s2.

Next, we use the kinematic equation for velocity in the y-direction: v_y(t) = v_{y0} + a_y*t, where v_{y0} is the initial velocity in the y-direction, a_y is the acceleration in the y-direction, and t is time. Similarly, we can find the position in the y-direction over time using y(t) = y_0 + v_{y0}*t + 0.5*a_y*t2, with y_0 being the initial position. For the x-direction, since there is no force, the object will move with a constant velocity, so the x position can be found with x(t) = x_0 + v_{x0}*t. By plotting these equations, we can determine the object's motion over a given time.

The path of the object can be determined by plotting y vs. x, which would show its trajectory. Since the force only acts in the y-direction, we expect this trajectory to be a parabola, with the object slowing down, coming to a stop, and reversing direction in the y-axis while moving at a constant speed in the x-axis.

User Pankaj Agrawal
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