Warm-up Draw graph, write brief question and answer

2. Horizontal Motion

Five principal motion variables vo – initial velocity vf – final velocity Δx – displacement (shown on formula sheet as x-xo) a – acceleration t - time

Key Points Signs are important for all variables (except time) When three out of five variables are known, the remaining variables can be solved for Always include units in the answer

The equations (Remember Δx = x – xo) Sometimes, you will need to use 2 of these equations so that you don’t have to solve a quadratic equation

Example #1 Example: A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it speeds up at 2.40 m/s2 a) How fast is the boat moving after accelerating for 5 seconds? Define positive to be moving out of the marina Starting point is breakwater, ending point is 5 seconds later What do I know? What do I want? vo= +1.50 m/s vf = ? a = +2.40 m/s/s t = 5 s 13.5 m/s

Example #1 cont b) How far did the boat travel during that time?

Can do the same thing with a graph! 13.5 m/s 1.5 m/s Total displacement = 7.50 + 30 = 37.5 m = Total AREA under the line.

Example #2 What do I know? What do I want? vo= +12 m/s Δx = ? Example: You are driving through town at 12 m/s when suddenly a ball rolls out in front of your car. You apply the brakes and begin slowing down at 3.5 m/s2. How far do you travel before coming to a complete stop? Positive is direction you are moving Start of motion is when brakes are applied, end of motion is when you stop What do I know? What do I want? vo= +12 m/s Δx = ? a = -3.5 m/s/s vf = 0 m/s 20.57 m

Example 3 Positive direction is direction spacecraft is moving Beginning of motion is when the retrorocket fires, end of motion is 215 km later (215000 m)

Example 4 - qualitative A bus driver makes an emergency stop by slamming on the brakes and skidding to a stop. How far would the bus have skidded if it had been traveling twice as fast? (in comparison to the 1st )

Example 5 – Last one! A model rocket is launched straight upward with an initial speed of 50 m/s. It speeds up with a constant upward acceleration of 2.0 m/s2 until the engine stops at an altitude of 150 m. How much time does it take for this to happen? Positive direction is up Beginning of motion is launch, end of motion is when engine stops