Goal: To understand linear motions

1. Goal: To understand linear motions Objectives: To understand the relationships between Distance and velocity To understand the relation ships between Velocity and acceleration To understand the relationships between Distance and acceleration

2. Now that we know what everything means, how do we use it? • First lets compare distance and velocity. • Lets see if you know how to do this already… • Person A travels at a constant velocity of 50 miles per hour west for 4 hours. • Person B travels at an average velocity of 50 miles per hour west for 4 hours. • How far do persons A and B travel (yes distance can have direction also)?

3. Two ways to do this! • 1) Unit conversion, if 1 hour = 50 miles (i.e. 50 miles per hour) you can convert hours to miles. • 2) Distance = average velocity * time • ONLY works if you have a constant or average velocity. If there is an acceleration this equation does not work.

4. Let try another, but in this case in 2 D • A plane is heading west at a velocity of 200 mph West. • A wind from the Gulf of Mexico blows at a rate of 70 mph in a direction that is 30 degrees North of West. The plane gets carried by the wind. • A) In 3 hours how far West does the plane travel? • B) In 3 hours how far North does the plane travel? • C) What is the total travel distance (i.e. magnitude) for the plane in 3 hours?

5. Changing velocity • If you change your velocity (even it if it just changing the direction) that is an acceleration. • However, how do we find the new velocity. • How do we find the acceleration. • First acceleration: • Acceleration = change in velocity / time

6. Another way • V = Vo + at • Example: • A car accelerates at a rate of 3 m/s2 for 4 seconds. • After the 4 seconds of acceleration the velocity is 23 m/s • What was the velocity of the car before the acceleration?

7. Run away truck! • A truck looses its breaks and accelerates down a hill at an acceleration of 2 m/s2 forward • The trucks initial velocity was 30 m/s forward. • What will the truck’s velocity be after 10 seconds? • To save himself the truck driver pulls onto a run away truck road – which is a common road on a mountain road. • Will the acceleration on the truck be negative or positive in the forward direction?

8. Save the truck! • Imagine that the truck starts at 50 m/s forward and the acceleration on this road in the is -5 m/s2 forward • What will the trucks velocity be after 2 seconds? • How long will it take for the truck to stop (I know, this one is tougher, but think about it)?

9. Distance vs. acceleration • The distance that an object will move – assuming constant acceleration – will be: • X = Xo + Vo t + ½ * a * t2 • Keep in mind sometimes a can be negative.

10. Example • For the run away truck, lets imagine it started at rest and accelerated at a rate of 2 m/s2 forward up to a velocity of 50 m/s forward (assume Xo is 0 m here) • A) How much time will it take the truck to get to 50 m/s forward? • B) How far will the truck move in this time?

11. Deceleration example • If the truck decelerates at 4 m/s2 (which means the acceleration is –4 m/s2 forward) then how much time does it take the truck to stop? • How far does the truck move in this time (take Xo to be 0 m again here)?

12. Example • You toss a ball straight up into the air at an initial velocity of 20 m/s from the roof of a 30 m tall building. • Do you want your positive direction to be up or down? • What do you want to set the initial position Xo to be? • A) How long will it take for the ball to hit the ground? • B) What height above the ground will the ball be after 3 seconds? • WATCH SIGNS AND DIRECTIONS FOR THIS PROBLEM!

13. A ball falls off of a cliff! • A) If the ball falls for 5 seconds how far will it fall? • B) What will the ball’s velocity be just before it hits the ground if it hits the ground at that point?

14. If we have some extra time: • Lets do a projectile question and put everything together. • A punter punts a football at a 30 degree angle above the ground from a starting height of 0.6 m above the ground. • If the punter kicks the ball with a total velocity of 20 m/s find: • A) What is the initial upwards velocity? • B) How long will the ball be in the air?

15. Conclusion • We have learned most of what there is to know about linear motion. • We have learned how to use distances, velocities, and accelerations to find other values – and how to find time. • The only way to make this harder is to add in a 2nd dimension – which we will do next lecture with projectiles.