Acceleration

Understanding Speed vs. Velocity  Speed is simply how fast  Velocity is how fast in a direction  Speed = distance/time  Velocity = displacement/time

Self check  The speedometer of a car moving east reads 100 km/h. It passes another car moving west at 100 km/h. Do they have same speed? Velocity?  Same speed but different directions so their velocities are different.  During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? Constant velocity?  Speed is constant but direction may not be constant so velocity may or may not be constant.

Velocity  speed in a given direction. Velocities in the same direction: (+) Add  + =  2m/s E + 1m/s E = 3m/s E Velocities in different directions: (-) Subtract  + =  2m/s E - 1m/s W = 1m/s E Examples EscalatorEscalator TreadmillTreadmill

Don’t be so negative  It is important Velocities have direction  Since we can have many different directions, in physics we usually use a + and – sign  Usually this corresponds to the graphing axis (x and y)

Acceleration  Acceleration - the rate of change in velocity.  Any time Velocity (Speed or direction) changes  acceleration = v final - v initial time We can usually feel Accelerations

Try It!  If a rocket blasts off at 200km/s N into space and after 8 sec. reaches a velocity of 550km/s N. What was the rocket’s acceleration after take off?  Step 1  acceleration = v final – v initial time  Step 2  acceleration = 550km/s – 200km/s 8 s  Step 3  acceleration = 43.8km/s/s or km/s 2

Deceleration  Deceleration – a decrease in velocity over time.  Same formula, just different name Deceleration is negative acceleration.

Try It!  If a car traveling at a velocity of 50 m/s and quickly stops in 3s for a red light, find the deceleration of the car?  Step 1  deceleration = v final – v initial time  Step 2  deceleration = 0m/s – 50m/s 3 s  Step 3  deceleration = -16.7m/s/s or m/s 2

Accelerating a Car  Gas Pedal If acceleration is positive, then velocity is increasing  Brake Pedal If acceleration is negative, then velocity is decreasing (deceleration)  What other way is there to accelerate your car?

ACCELERATION 1. The slope of a velocity-time graph is acceleration just as the slope of a displacement-time graph is velocity. No slope. No acceleration. a. If the graph is linear, acceleration is uniform or constant and avg. acceleration = instantaneous acceleration. b. If the graph is a curve. The acceleration is different at every point, but instantaneous acceleration on this graph is still the slope at a point on the curve.

Remember! Acceleration is a Vector  This means that it can have a sign (+ or -).  So, a velocity vs time graph with a positive slope is a (+) acceleration graph and a velocity vs time graph with a negative slope is a deceleration graph.

Distance-Time Graph  Acceleration is indicated by a curve on a Distance-Time graph.  Changing slope = changing velocity Graphing Acceleration

 A Distance vs. Time Graph Acceleration is represented by a curved line.  A Speed vs. Time Graph Acceleration is represented by a straight diagonal line.

Graphing Accelerated Motion Speed-Time Graph  slope =  straight line =  flat line = acceleration  + = speeds up  - = slows down constant accel. no accel. (constant velocity)

Speed-Time Graph Specify the time period when the object was...  slowing down 5 to 10 seconds  speeding up 0 to 3 seconds  moving at a constant speed 3 to 5 seconds  not moving 0 & 10 seconds

Graphing (+) & (-) Acceleration

Why is it + Acceleration?

Why is it (–) Acceleration?

Why is there no Acceleration?

Graphing the motion of a Ball thrown Upward

Breaking Down the Throw: Acceleration of the Upward Leg

Breaking Down the Throw: Acceleration of the Downward Leg

Position vs Time Graph of Constant Positive (+) Acceleration

Position vs Time Graph of Constant Positive Negative (-)Acceleration

Warm-Up  What is acceleration?  What is the shape of a distance- time graph for accelerated motion?  What is the shape of a Speed-time graph for accelerated motion?  Why are they different?

Momentum

 Momentum – is equal to the mass of an object multiplied by its velocity.  How hard it is to stop a moving object  All moving objects have momentum.

Momentum “Inertia in Motion” Momentum of an object is, (Momentum) = (Mass) X (Velocity) P = M V or M V = P Examples of objects with a large momentum are supertanker (large mass) and bullet (large velocity).

Check Yourself A 2 ton car, going 60 m.p.h. hits a 5 ton truck, going 20 m.p.h.. Which vehicle, the car or the truck, has greater momentum? The car because (2)x(60) = 120 and (5)x(20) = 100. What would the car’s speed have to be for the momentums to match? Fifty m.p.h. since (2)x(50) = (5)X(20). Aren’t you forgetting something? The direction of velocity. How does that matter? Rear-end crash not same as a head-on crash. More about this when we do collisions.

Conservation of Momentum  Law of Conservation of Momentum – states that the total momentum of any group of objects remains the same unless outside forces act on the object.

Recoil Momentum conservation also explains recoil (MASS) x (velocity) (mass) x (VELOCITY)

Wrap Up!  What is momentum?  What is the law of conservation of momentum?  Using the formula for calculating momentum, determine the units of measurement?