While standing on a horizontal frictionless surface a 50.0 kg student pushes against a wall with an average force of 125 N to the right for 0.110 s. Calculate the velocity of this student at 1.110 s.
My answer: Vf = 0.275 m/s
My solutions book has Vf = -0.275 m/s OR 0.275 m/s to the left.
My question is where does the negative or the "to the left" come from? My understanding is that "right" is positive.
Thanks.
In physics, we typically assign a positive direction as the direction of motion or the direction of the force being applied. In this case, the student is pushing against the wall to the right with a force of 125 N. Therefore, we can take the right direction as positive.
However, when the student is released from the wall at 1.110 s, there is no longer any force acting in the right direction. The only force acting on the student is the force of gravity, which acts vertically downwards. Without any force to the right, the student will start moving in the opposite direction, to the left.
Because the student's velocity is changing direction, we assign a negative sign to indicate the change in direction. So, in this case, a velocity of -0.275 m/s or 0.275 m/s to the left means that the student is moving in the opposite direction of the initial force applied to the wall.
The negative sign or "to the left" in this context indicates the direction of motion. In physics, it is common to assign a positive direction and a negative direction to represent motion in opposite directions along a line.
In this scenario, let's consider "to the right" as the positive direction. When the student pushes against the wall with a force, the force applied by the student is in the positive direction. This force causes the student to accelerate in the positive direction initially.
However, once the force is no longer being applied, the student will start to decelerate and come to a stop. At the time you are trying to calculate the velocity (1.110 s), the student is actually moving in the opposite direction to the force applied by the student (i.e., to the left). Therefore, the velocity is negative to denote the direction opposite to the positive direction or "to the left."
So, when you calculated the velocity to be 0.275 m/s, it indicates that the student is moving with a speed of 0.275 m/s in the opposite (or negative) direction to the positive direction. In other words, the student is moving at a speed of 0.275 m/s to the left.
In summary, the negative sign before the velocity or the statement "to the left" indicates the direction of motion, which is opposite to the positive direction (to the right) in this case.