Forces and Motion
Speed and Velocity
Description
You’re going on a trip. You plan to leave at 7am. But you actually leave at 7:15am. To pass the time, you decide you’d like to figure out how fast you went during the trip. You could record your speedometer reading every second and take an average at the end of your trip but this would be cumbersome (and dangerous if you are driving!). So you decide to try another method. At the beginning of your trip, the odometer on your car reads 11,441 miles. When you arrive at your destination, your watch reads 2:35pm and your odometer reads 11,795 miles. So, you would like to know how fast you were going and you go about figuring this out…
Equation
velocity = distance__________time
v = d—t
1.1
↔ Distance Traveled = last odometer reading – initial odometer reading
= 11,795 miles – 11,441 miles = 354 miles
↑→ Elapsed Time = final watch reading – initial watch reading
= 2:35 pm – 7:15 am = 7 hours 20 minutes
↑ Speed = distance traveled / elapsed time
= d/t = 354 miles / 7.33 hours = 48.3 miles / hour
Note: 20 minutes out of 1 hr (60 min) is 20/60 = 2/6 = 1/3 = 0.33 hr
So Speed = change in distance / change in time. For this reason, all…ALL speeds are AVERAGE SPEEDS. You may have stopped for gas, stopped at a stoplight, spent time cruising down the highway and slowed down in a residential neighborhood. It all gets averaged together. You must always figure in a change in time and therefore, a change in distance, so the equation is just s = d/t.
Speed is a scalar quantity; that is, it only has a magnitude or size. Velocity, on the other hand, is a vector quantity. It has both magnitude (e.g. 50 miles per hour) AND direction (e.g. south). So you can say your average speed is 50 miles per hour but your average velocity would be 50 miles per hour to the south. In science we most commonly use velocity, so its equation is:
velocity =distance—————time v = d— t
Police never give you a ticket for velociting because they don’t care which direction you are driving, just how fast you are going.
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