MECHANICS – Linear Motion Motion is everywhere ! But how does one describe the motion around them ?

Motion is described by rate RATE is a quantity divided by time. It tells how fast something happens Or how much something changes in a certain amount of time. Motion is described by rates known as: Speed, Velocity, and Acceleration

So what’s Linear Motion ? Linear Motion is the simplest form of motion It is motion along a straight line path. Horizontally or Vertically

Motion is Relative … huh? Everything is moving … The Earth rotates and moves around the sun The sun moves around the center of the Milkyway galaxy So when a movement is described, it is discussed with respect to some other object or to the surface of the Earth.

SPEED SPEED is a measure of how fast something is moving. SPEED is the rate of distance covered divided by time. s = d / t UNITS of Speed : miles / hr. kilometers / hr. cm / sec meters / sec. light-years / century

Different Types of Speed Instantaneous Speed - Think of the speed of a car in traffic. stop and go, 50 mph to 15 mph etc… Average Speed = total distance covered. time interval Example : 240 km driven in 4 hr. is what average speed? 240 km 4 hr 60 km / hr

Approximate speeds in different units 20 km / hr = 12 mi / hr = 6 m / sec 40 km / hr = 25 mi / hr = 11 m / sec 60 km / hr = 37 mi / hr = 17 m / sec 80 km / hr = 50 mi / hr = 22 m / sec 100 km / hr = 62 mi / hr = 28 m / sec 120 km / hr = 75 mi / hr = 33 m / sec 140 km / hr = __ mi / hr = __ m / sec

Questions The speedometer in every car also has a trip odometer that records the distance traveled. a. If the trip odometer reads zero at the beginning of. a trip and 35 km a half hour later, what is the. average speed ? b. Would it be possible to attain this average speed. and never exceed a reading of 70 km/hr on the. speedometer ? No, not if the trip starts at rest and ends at rest, because any intervals with an instantaneous speed less than 70 km/hr would have to be compensated with instantaneous speeds greater than 70 km/hr to yield an average speed of 70 km/hr. In practice, average speeds are usually a lot less than th etop instantaneous speed. = 70 km / hr total distance covered Average speed = time interval 35 km 0.5 hr =

Questions If a cheetah can maintain a constant speed of 25 m/sec, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute ? A little thought shows that this is simply a rearrangement of : s = d / t then the distance covered is : distance = average speed x time interval or distance = (25 m/sec) x (10 sec) = 250 m and distance = (25 m/sec) x (60 sec) = 1500 m Therefore, in 10 sec the cheetah will cover 250 m, and in 1 minute (60 sec) it will cover 1500 m, more than 15 football fields!

VELOCITY Velocity is speed in a given direction Example : 45 km / hr, northeast 9.8 m / sec straight down lickety split that-a-way Constant Velocity means traveling at the same speed in the same direction

VELOCITY Changing Velocity A car going in a circle can be moving at a constant speed, but because it is NOT moving in a constant direction, is not moving with a constant velocity. The velocity is CHANGING.

Question A car traveling northward at 60 km/hr. It passes another car traveling southward at 60 km/hr. Do both cars have the same speed ? Do they have the same velocity ? Both cars have the same speed, but their velocities are opposite because they are moving in opposite directions.

ACCELERATION Acceleration = The rate of change in velocity Acceleration means speeding up as well as slowing down (negative acceleration or deceleration) a = v 2 -v 1 t 2 -t 1 change of velocity Time interval _______

Acceleration : Example The Mr. Freeze ride at Six Flags over Mid America takes the rider from 0 km / hr to 142 km / hr. in 2 seconds. What is the acceleration? GIVEN : s = 142 km / hr t = 2 sec a = s / t FIND : a = ? a = s / t = 142 km / hr / 2 sec = 71 km / hr / sec