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 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 = vf2-vi2 2∆d ∆d = vi∆t + 1a∆t2 2

Example 1 A fast Mustang does quarter mile (402.3 meters) in 15 seconds. What is his acceleration? How fast is he going when he crosses finish line? d = 402.3m t = 15s v = ? a = ? v = d/t = 402.3m/15s = 26.82 m/s a = v/t = 26.82m/s = 1.78 m/s2 15s a = vf-vi ∆t 1.78 m/s2 = vf -26.82 m/s 15s vf = ? (1.78 m/s2)(15s) = vf -26.82 m/s (1.78 m/s2)(15s) + 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 50km/h to 65km/hr, while a truck goes from rest to 15km/hr in a straight line in the same time period. What is the acceleration of each vehicle? Which vehicle has the greater acceleration? a = vf-vi ∆t 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 = ? acar = (65km/h)-(50km/h) = 10791.4 km/h2 .00139h atruck = (15km/h)-(0km/h) = 10791.4 km/h2 SAME accelerations! Convert time from s to h 5s min h = .00139 h 60s 60min

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? a = vf2-vi2 2∆d a = -8.19 m/s2 Vi = 22.35 m/s Vf = 0 d = 30.48 m a = ? 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/s2 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? a = vf-vi ∆t 3m/s2 = vf – 15m/s 18s vi = 15 m/s a = 3 m/s2 t = 18 s vf = ? (3m/s2)(18s) = vf – 15m/s (3m/s2)(18s) + 15m/s = vf 69m/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 -9.8m/s2 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.