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ti = initial time • tf = final time • ∆t = time interval = tf - ti • xi = initial position • xf = final position • ∆x = displacement = xf– xi • distance = s∙∆t • s = speed
Motion Diagram • Motion diagrams are a pictorial description of an object in motion. (Ex)
Changing Velocity (Acceleration) • Speeding up = going faster and faster = acceleration (a) Velocity increases at a constant rate (Ex) 10 m/s, 15 m/s, 20 m/s, 25 m/s, 30 m/s (b) Velocity increases at a decreasing rate (Ex) 10 m/s, 15 m/s, 19 m/s, 22 m/s, 24 m/s, 25 m/s 2. Slowing down = going slower and slower = deceleration (Ex) 10 m/s, 8 m/s, 6 m/s, 4 m/s, 2 m/s 3. Changing the direction (Ex) 10 m/s, -10 m/s Caution: Outside the classroom, acceleration means to speed up
Constant Acceleration • The velocity increases at a constant rate (Ex) A car’s velocity at 1:00 pm is 0 mph; at 1:01 pm, 20 mph; at 1:02 pm, 40 mph; 1:03 pm, 60 mph; 1:04 pm, 80 mph • The velocity decreases at a constant rate (Ex) A car’s velocity at 1:05 pm, 80 mph; at 1:06 pm, 70 mph; at 1:07 pm, 60 mph; 1:08 pm, 50 mph; 1:09 pm, 40 mph
You must be able to tell the velocity is changing... • from the motion diagram • from the velocity vs. time graph 3. from the table of: (a) velocity vs. time (b) position vs. time
* Cars with leaky oil – PDF file..\Physics Labs & Worksheets • Is this what you got? ..\Cars with leaking oil.xlsx
Average Acceleration • a vector quantity (Ex) A car’s velocity at 11:00 AM was 90 km/hr and its velocity changed to 110 km/hr at 11:03 AM. What is the average acceleration of this car?
Which shows acceleration? • displacement vs. time
velocity and acceleration • Determine the acceleration in each motion diagram. vi = 5 m/s vf = 7 m/s vi = 5 m/s vf = 3 m/s vf = -7 m/s vi = -5 m/s vf = -3 m/s vi = -5 m/s
More on Motion with Constant Acceleration velocity, m/s m = ā vi time, s
Constant (Average) Acceleration Quick Review: For an object moving at a constant velocity,
Relating Velocity & Acceleration • “+” velocity and “+” acceleration = Demo • “+” velocity and “–” acceleration = Demo • “‒” velocity and “+” acceleration = Demo • “‒” velocity and “‒” acceleration = Demo
Position, Velocity & Acceleration acceleration, m/s2 0 time, s
Practices velocity, m/s A B E D 0 time, s C
Examples • A train moving with a velocity of 51 m/s east undergoes an acceleration of -2.3 m/s2 as it approaches a town. What is the velocity of the train 5.2 s after it has begun to decelerate? • After being launched, a rocket attains a speed of 122 m/s before the fuel in the motor is completely used. If you assume that the acceleration of the rocket is constant at 32.2 m/s2, how much time does it take for the fuel to be completely consumed?
3. A car traveling at 21 m/s misses the turnoff on the road and collides into the safety guard rail. The car comes to a complete stop in 0.55 s. a) What is the average acceleration of the car? b) If the safety rail consisted of a section of rigid rail. the car would stop in 0.15 s. What would be the acceleration in this case? 4. A cheetah can reach a top speed of 27.8 m/s in 5.2 s. What is cheetah’s average acceleration?
Position, Velocity & Acceleration • Given: • (position or displacement missing) • (final velocity missing) • (time missing) • In all of above equations, ∆t=tf if ti= 0 • See Pg 52-56 for the derivation
Words to Formulas • decide the positive direction • to right, to east, or up: positive • to left, to west, or down: negative • come to stop or to rest: vf= 0 • from rest: vi = 0 • slows down: +v and ‒a, or ‒v and +a • speeds up: +v and +a, or ‒v and ‒a • at constant velocity: a = 0 • going down or up a hill: a ≠ 0 • the sign of ∆v = the sign of ∆d • tf = ∆t = a positive number (ti = 0) • df= ∆d (di = 0) • at the moment of reversing direction, v = 0 and a ≠ 0 • how long to take: ∆t • how far: ∆d • from A to B: A = initial; B = final
Examples • Suppose a car rolls down a 52.0-m long inclined parking lot and is stopped by a fence. If it took the car 11.25 s to roll down the hill, what was the acceleration of the car before striking the fence? • A sky diver in free fall reaches a speed of 65.2 m/s when she opens her parachute. The parachute quickly slows her down to 7.30 m/s at a constant rate of 29.4 m/s2. During this period of acceleration, how far does she fall?
3. A child rolls a ball up a hill at 3.24 m/s. If the ball experiences an acceleration of 2.32 m/s2, how long will it take for the ball to have a velocity of 1.23 m/s down the hill? 4. A cheetah can accelerate from rest to a speed of 27.8 m/s in 5.20 s. The cheetah can maintain this speed for 9.70 s before it quickly runs out of energy and stops. What distance does the cheetah cover during this 14.9-s run?