3 agenda lecture practicing physics: p8, p10 lab: measurement of constant velocity and constant acceleration

3 linear motion speed and velocity changing velocity distance traveled

motion measured with respect to Earth’s surface unless otherwise indicated unit: meters/second m/s speed is the scalar of motion velocity is the vector of motion

speed speed = rate of travel average speed = (distance traveled)/time “speed” assumes “time” is small “average speed” assumes “time” is large (i.e., speed may vary) velocity = speed and direction

Velocity Velocity is speed in a given direction (velocity is a vector, speed is a scalar) frequently we use “+” to mean “upward” or “rightward” and “-” to mean “leftward” or “downward” Note that an object may have constant speed but changing velocity

Displacement displacement = change in position when velocity is constant (unchanging), the displacement = vt, where v = velocity and t = time. Example: velocity = -3m/s, time = 2s, the displacement is vt = (-3m/s)(2s) = -6m, i.e., has moved 6 meters in leftward direction ( - being left, + being right)

Acceleration Acceleration = change of velocity time interval SI unit: m/s/s The motorcycle rider experiences an acceleration in each case shown. What are the directions for each case?

Question Can an object have zero velocity but non-zero acceleration? Answer: Yes! Eg. Throw a ball up in the air – at the top of its flight, as it turns around it has momentarily zero speed but is changing its direction of motion, so has non-zero acceleration

Free fall falling under influence of gravity alone (no air resistance, etc.) a = “g” = 10m/s/s independent of mass (free-fall) from rest: v = gt.

object thrown upward slows at a rate of g… then has zero velocity as it changes its direction from up to down. then falls speeding up at a rate of g. equal elevations have same speed (but opposite direction)

Free-Fall Distance initial velocity = 0 final velocity = gt average velocity = ½ (0 + gt) = ½gt. distance d = (average velocity)x(time) d = ½gt x t  d = ½gt2. Example: after 3.0 seconds: d = ½(10)(3)2 = 5x9 = 45 meters

Application: “Hang-time” of jumpers Michael Jordan’s best hang-time was 0.9 s Round this to 1 s. How high can he jump? Use d = ½ g t2 . For 1 s hang-time, that’s ½ s up and ½ s down. Substituting ½ = 0.5 seconds into the distance equation d = ½ (10) (0.5)2 = 1.25 m This is about 4 feet!

Question (to think about…)

For example: Cities are 600 km apart, and plane’s airspeed is 300 km/h (relative to still air). Time each way with no wind is 2 hours. Round trip time is 4 hours. If a 100 km/h tailwind is blowing, the groundspeed is 400 km/h one way and 200 km/h the other. The times are: (600 km)/(400km/h) = 1.5 h and: (600 km)/(200km/h) = 3.0 h The round trip now takes 4.5 hours—longer than with no wind at all.

3 summary speed is the rate of travel velocity is speed and direction acceleration is the rate of change of velocity for free-fall: a = g = 10 m/s/s v = gt d = ½gt2.