## Position and Displacement Vectors, Speed vs. Velocity

### Calculating the coordinates and direction of displacement and position vectors

Gerry, the gerbil, walks 55 cm in the positive y-direction. After this, he is located 95 cm from the origin at an angle of 50 degrees from the positive x-axis towards the positive y-axis, as shown in the figure.

### Practicing how to find the coordinates of a vector for its length and direction and vector subtraction

Deserted on a deserted Island, you spot a slightly exposed tin can under a tree. Upon opening it, you find it is instructions to a treasure. It reads:

Find the coordinates of the treasure.

### Practicing how to find the total distance traveled, displacement vector, the distance between two points, average speed, and velocity of a set of vectors

An amusement park roller coaster starts out on a level track 5 m long and then goes up a 25 m incline at an angle of 30° up from the horizontal. Finally, it goes down a 15 m ramp with an incline of 40° below the horizontal. Consider the entire trip to when the coaster has reached the final ramp’s bottom. Assume it takes one minute to reach the end of the last ramp.

### Practicing how to find the total convert speed to velocity, velocity to displacement, and vice versa

During the middle of a family picnic, Barry Allen received a message that their friends, Bruce and Hal, needed to be saved. Barry promised his partner, Iris, he would return in exactly 5 minutes. From that picnic location, Barry runs at a speed of 600 m/s  for 2 minutes at a heading of 35° north of west to save Bruce. He then changed his heading to 30° west of north but slows down to 400 m/s   and runs for 1 minute to save Hal. (The speed changes are essentially instantaneous and not part of solving this problem).

## Graphical Analysis

### Generating displacement vs. time and acceleration vs. time from a velocity vs. time plot.

The figure shows a plot of a car’s velocity as a function of time.

## 1-D Kinematics of Constant Acceleration and problem solving strategies

### Exam Level Practice Problem

Two objects start from the same location and time but have different accelerations and initial velocities. We are asked to calculate the final location they meet again, and the time this process takes. In addition, we need to sketch the position vs. time (x-t) plot of the objects.

## 2-D Kinematics and Projectile Motion

### Ultimate Level Practice Problem

Two objects, one with a contact speed, the other one with a constant speed race. First, we are asked to work on a 1D kinematic problem; then, we take the final values of part (a) and use them as the initial values of part (b). In part (b), we work on a complex projectile motion with a contact acceleration along the x and y-axis.