Acceleration Units of acceleration Acceleration is a vector

Acceleration • Units of acceleration: • Acceleration is a vector quantity. • A positive acceleration describes a change in velocity in the positive direction. • A negative acceleration (deceleration) describes a change in velocity in the negative direction.

Velocity vs. Time Graph • The rate at which velocity changes over an interval of time is known as average acceleration, aav. • Mathematically, • The slope of a v-t graph describes the acceleration of the object in motion.

• Negative velocity means there is a – displacement…which means the direction has changed • A = going towards home with increasing velocity and constant acceleration • B = going away from home with increasing velocity and constant acceleration

• You kick a soccer ball up a hill. Describe the motion based on the graph. • How far did the ball travel up hill? • How far did it travel down hill?

Constant Acceleration

Acceleration Equations a = vf-vi ∆t a = vf 2 -vi 2 2∆d ∆d = vi∆t + 1 a∆t 2 2

Example 1 • A fast Mustang does quarter mile (402. 3 meters) in 15 seconds. What is his acceleration? d = 402. 3 m t = 15 s v=? a=? v = d/t = 402. 3 m/15 s = 26. 82 m/s a = v/t = 26. 82 m/s = 1. 78 m/s 2 15 s • How fast is he going when he crosses finish 1. 78 m/s = v -26. 82 m/s line? a = v -v f vf = ? ∆t i 2 f 15 s (1. 78 m/s 2)(15 s) = vf -26. 82 m/s (1. 78 m/s 2)(15 s) + 26. 82 m/s = vf 53. 52 m/s= vf

Example 2 • In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/hr, while a truck goes from rest to 15 km/hr in a straight line in the same time period. What is the acceleration of each vehicle? Which vehicle has the greater acceleration? CAR t=5 s vi = 50 km/h vf = 65 km/h a=? TRUCK t=5 s vi = 0 km/h vf = 15 km/h a=? Convert time from s to h 5 s min h =. 00139 h 60 s 60 min a = vf-vi ∆t acar = (65 km/h)-(50 km/h) = 10791. 4 km/h 2. 00139 h atruck = (15 km/h)-(0 km/h) = 10791. 4 km/h 2. 00139 h SAME accelerations!

Example 3 • Truck slams brakes at 50 MPH (22. 35 m/s). Stops in 100 ft (30. 48 meters). How much acceleration/deceleration did the truck have? Vi = 22. 35 m/s Vf = 0 d = 30. 48 m a=? a = vf 2 -vi 2 2∆d a = -8. 19 m/s 2 v (m/s) t (s) • What would a graph of the situation look like?

Example 4 • A driver traveling at 15 m/s sees Miley Cyrus standing in the middle of the road grabbing her crotch. He immediately accelerates at 3 m/s 2 in an attempt to run her over. If he keeps this acceleration for 18 seconds, how fast is he going when he plows her over? vi = 15 m/s a = 3 m/s 2 t = 18 s vf = ? a = vf-vi ∆t 3 m/s 2 = vf – 15 m/s 18 s (3 m/s 2)(18 s) = vf – 15 m/s (3 m/s 2)(18 s) + 15 m/s = vf 69 m/s = vf

Free Fall • For all objects in free fall near the surface of the earth, – acceleration due to gravity is a CONSTANT equal to -9. 8 m/s 2 • The initial velocity (vi ) of an object that is: - launched upward is POSITIVE. - dropped is ZERO. - launched downward is NEGATIVE. • The velocity of a free-falling object at its highest point of motion is ZERO. • The time for an object to rise from its release point is EQUAL TO the time for it to fall back to its release point.

Example 4 • Drop a bowling ball off a balcony (5 meters). How long does it take to hit the ground? • How fast is it going when it hits the ground.