Kinematic: a study of motion described by speed or velocity without concern about what causes the motion.

Speed: a measure of how fast an object moves without concern about the direction of the motion. Speed of an object is the distance covered by the object in a time interval.

Average Speed: if the speed of an object is changing in an time interval its average speed is defined by

     Average Speed = Distance Traveled / Time Elapsed

                    Vav = DL / Dt

Instantaneous Speed: the speed of an object at a particular moment or instant, i.e.,

    V = (DL/Dt) as Dt approaches zero = dL/dt = the slope of the curve L versus t

Figure 1 shows an object moving for a total of 7 seconds. For the first 5 seconds it moves at 10 m/s; for the next 2 seconds it moves at 20 m/s. What is its instantaneous speed and its average speed?

Instantaneous speed is constant at 10 m/s during the first 5 seconds, and then jumped to 20 m/s during the next 2 seconds.

Average speed during the entire 7 seconds is [10 m/s x 5 s + 20 m/s x 2 s] / (5 s + 2 s) = 12.85 m/s.

Figure 2 shows an object moving variable speeds at all times. Identify the time intervala at which the speed is positive, zero, and negative.

Velocity: velocity of a moving object is a vector quantity V: the magnitude of the vector is the speed denoted by V, and the direction of the vector is the direction of the velocity.

    Average Velocity = Vav = Displacement (S) / time elapsed (T) = S / T

Displacement: displacement of a moving object is specified by the distance and direction it traveled.

Fig. 3 shows the displacement vectors of an object start from the origin (0,0) moves north-east to point A at (2,2) and then moves due north to point B at (5,2), then due east to point C to (5,5) and then moves south-east to point D at (7, 2) at the end. There are 4 displacement vectors.

If the object moves at a constant speed and takes one second to travel each of the 4 displacements, determine the velocities of the motion.

d1 =displacement from (0,0) to (2,2) = (2**2 + 2**2)**1/2 = 2.828 m in a N-E direction.
d2 =displacement from (2,2) to (5,2) = 3.0 m due north.
d3 =displacement from (5,2) to (5,5) = 3.0 m due east.
d4 =displacement from (5,5) to (7,2) = (2**2 + 3**2)**1/2 = 3.605 m in a S-E direction.

The velocities of the object:

V1 = 2.828 m/s in the north-east direction during the first second;
V2 = 3.0 m/s due north during the second second;
V3 = 3.0 m/s due east during the third second;
V4 = 3.605 m/s in a south-east direction during the fourth second.

The average velocity during the 4-second interval is shown in dash arrow = (2**2 + 7**2)**(1/2) / 4 = 1.82 m/s in a north-east direction of the dashed arrow.

Fig. 4 shows the trajectory of the moving object. It moves from (0,0) along a complicated trajectory and ended at (2,7) in a total of 2 seconds. What is its average velocity? Its instantaneous vlocity changes at all times and can be determined by the slope of the trajectory at each point on the trajectory.

The direction of the average velocity is given by the dashed arrow in Fig. 4 which is in the same direction as the average velocity in Fig. 3.

The magnitude of the average velocity in Fig. 4 is 3.64 m/s which is exactly 2 times the magnitude of the average velocity in Fig. 3. How do you know?

Relative Motion:

Velocity is a vector. Therefore the velocity V of a boat in the river is the vector sum of the velocity VB of the boat relative to the water and the velocity VR of the water flow in the river. The magnitude of the velocity is V = (5**2 + 3**2)**0.5 = 5.83 m/s, in the direction as shown in the diagram.