What is velocity?

the average velocity of an object does not tell us anything about what happens to it between the starting point and ending point

For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he goes to the back of the plane. the smaller the time intervals considered in a motion, the more detailed the information.

Average velocity=

the change in position divided by the time of travel change in x/ change in t= Xf-Xo/Tf-To - if the starting time To is taken to be zero then the average velocity is written as below: Vavg= change in x/t

Example: an airplane passenger took 5 seconds to move -4 meters, where the negative sign indicates the displacement is toward the back of the plane. His average velocity can be written

Vavg= change in x/t = -4m/5s=-.8m/s - the minus sign indicates the average velocity is also toward the rear of the plane

velocity=

a large displacement in a small amount of time means a large velocity and that velocity has units of distance divided by time, such as miles per hour or kilometers per hour

velocity is a vector

because displacement is a vector - has both magnitude and direction -m/s

Example 1: Disoriented iguana. An iguana with a poor sense of spatial awareness is walking back and forth in the desert. First the iguana walks 12 meters to the right in a time of 20 seconds. Then the iguana runs 16 meters to the left in a time of 8 seconds. Assume that rightward is the positive direction.

- To find the average speed we take the total distance traveled divided by the time interval - average speed= distance traveled/ time interval= 12.0m +16.0m/ 20s+8s - average speed = 28.0m/28.0s - average speed= 1 m/s - to find the average velocity we take the displacement x divided by the time interval - average velocity= displacement/time interval= -4.0m/28.0s - average velocity= -1/7 m/s

Instantaneous speed at time t=4s Image on page 13

- instantaneous speed is the speed at a given moment in time and will be equal to the magnitude of the slope. Since the slope at t= 4s is equal to zero, the instantaneous speed at t= 4s is also equal to zero.

What does speed mean

- speed has no direction -speed is scalar - instantaneous speed is the magnitude of instantaneous velocity

For example, if you drive to a store and return home in half an hour and your car's odometer shows the total distance traveled was 6km, then your average speed was 12km/hr

- your average velocity, however, was zero because your displacement for the round trip is zero. - displacement is change in position and, thus, is zero for a round trip. Thus average speed is NOT simply the magnitude of average velocities

Average speed between t= 0 s to t= 6s Image on page 13

Average speed is defined to be the distance traveled per time. The distance is the sum of the total path length traveled by the dolphin, so we just add up all the distances traveled by the dolphin for each leg of the trip. Vavg= distance traveled/ change in t= 12m+0m+4m/6s-0s= 16m/6s Vavg= 8/3 m/s

average speed, however, is very different from average velocity

Average speed is the distance traveled divided by elapsed time. - so while the magnitudes of the instantaneous speed and velocity are always identical, the magnitudes of average speed and velocity can be very different. - since distance traveled can be greater than the magnitude of displacement, the average speed can be greater than the magnitude of the average velocity

Example 2: Hungry dolphin A hungry dolphin is swimming horizontally back and forth looking for food. image on page 13

Average velocity between time t=0 to t=6s Average velocity is defined to be the displacement per time Vavg= change in x/ change in t=0m-8m/6s-0s=-8m/6s V avg= -4/3m/s

Instantaneous velocity at time t= 1s image on pg 13

Instantaneous velocity is the velocity at a given moment and will be equal to the slope of the graph at that moment. To find the slope at t=1s we can determine the "rise over run" for any two points on the graph between t=0s and t=3s (since the slope is constant between those times). Choosing the times t=25 and t= 0s, we find the slope as follows, V instantaneous= slope= X2-X0/T2-T0 V instantaneous= 0m-8m/2s-0s= -8m/2s Vinstantaneous= -4 m/s

instantaneous velocity

velocity at a specific moment - a car's speedometer, for example, shows the magnitude- but not the direction- of the instantaneous velocity of the car. Police give tickets based on instantaneous velocity, but when calculating how long it will take to get from one place to another on a road trip, you need to use average velocity. - instantaneous velocity, v, is simply the average velocity at a specific instant in time or over an extremely small time interval