Part 1 The displacement Vector Consider again the displacement vector ? = ? 0, w
ID: 2214867 • Letter: P
Question
Part 1 The displacement VectorConsider again the displacement vector
? = ? 0,
which represents a change in position and is formed by subtracting the initial-position vector from the final-position vector.
To calculate the displacement, we subtract like Cartesian components so that the displacement vector has the following form.
? = ?x + ?y (1)
Part 2 The Velocity Vector
Velocity must be a vector. We can form the average velocity by dividing the displacement vector by the time that it takes to make the displacement.
average velocity (2)
The ?x/?t is the x-component, and similarly ?y/?t is the y-component. The velocity components are given by the following.
(3)
Note that ?t does not have any direction associated with it, so the average velocity vector must point in the same direction as the total-displacement vector.
The acceleration is also a vector and is defined by taking the change of the velocity in time.
acceleration (4)
Note that the direction of the acceleration is the same as the direction of the change in the velocity, and so it is not necessarily in the same direction as the velocity.
A truck starts out at position x = 2.7 mi and y = 5.4 mi and winds up at position x = 4.5 mi, y = 2.2 mi. The truck made the displacement in 11 minutes.
(a) Find the average velocity of the truck in miles per hour.
magnitude mph
direction
Explanation / Answer
b) vx=(4.5-2.7)/(11/60)=9.82 miles/hr
vy=(2.2-5.4)/(11/60)=-17.45 miles/hr
a) Magntude=20 miles/hr
Direction= Tan-1(-17.45/9.82)=-60.6 degrees or at an angle of 299.4 degrees with the x axis counterclockwise.