A student begins at rest and then walks north at a speed of v1 = 0.85 m/s. The student then turns south and walks at a speed of v2 = 0.26 m/s. Take north to be the positive direction
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now what?
For example for how long and what is the question?
To find the student's overall displacement, we need to break down the motion into two parts: the northward motion and the southward motion.
Step 1: Northward Motion
The student walks north at a speed of v1 = 0.85 m/s. Since north is the positive direction, the velocity is positive. Let's assume the student walks for a time t1.
Displacement during northward motion = Velocity of northward motion × Time taken for northward motion
Displacement during northward motion = v1 × t1
Step 2: Southward Motion
After turning south, the student walks at a speed of v2 = 0.26 m/s. Since south is the opposite direction, the velocity is negative. Let's assume the student walks for a time t2.
Displacement during southward motion = Velocity of southward motion × Time taken for southward motion
Displacement during southward motion = -v2 × t2 (negative because south is the opposite direction)
Step 3: Overall Displacement
To find the overall displacement, we need to subtract the southward displacement from the northward displacement. Since the directions are opposite, we can add the magnitudes.
Overall Displacement = Displacement during northward motion + Displacement during southward motion
Overall Displacement = v1 × t1 + (-v2) × t2
Note: The negative sign in front of v2 is taken into account to indicate the direction of south.
Remember to multiply the speeds by the respective times taken for each motion to get the total displacements.
To find the net displacement of the student, we need to calculate the total distance traveled in the north and south directions separately, and then subtract the distance traveled in the south direction from the distance traveled in the north direction.
Let's assume that the student walks for a time duration of t1 in the north direction and a time duration of t2 in the south direction.
In the north direction, the student's speed, v1, is given as 0.85 m/s. So, the distance traveled in the north direction is equal to the product of the speed and time: d1 = v1 * t1.
Similarly, in the south direction, the student's speed, v2, is given as 0.26 m/s. So, the distance traveled in the south direction is equal to the product of the speed and time: d2 = v2 * t2.
As the student starts from rest, the time taken in the north direction will be equal to the time taken in the south direction: t1 = t2 = t.
Now, we can express the distance traveled in terms of time. Since the speed is constant, we can use the equation d = v * t.
Therefore, d1 = v1 * t and d2 = v2 * t.
To find the net displacement, we subtract the distance traveled in the south direction from the distance traveled in the north direction: displacement = d1 - d2.
Substituting the values, we have:
displacement = (v1 * t) - (v2 * t)
= t * (v1 - v2)
So, the net displacement of the student is equal to the time taken multiplied by the difference in velocities: displacement = t * (v1 - v2).