Acceleration Physics Montwood High School R. Casao

Acceleration Defined Acceleration is defined as the change in velocity per change in time. Velocity is speed and direction of motion. If speed changes, an acceleration is definitely occurring. Acceleration involves a: –change in speed. –change in direction. –change in speed and direction.

–Consider a car traveling at a constant 40 mph on a long straight road. –The car is NOT acceleration because neither its speed or direction is changing. The car did accelerate to get its speed up to 40 mph, but did not accelerate after reaching 40 mph. –Consider a car driving around a circular track at a constant speed. –The car IS accelerating. The speed is not changing, but the direction of motion is changing. The velocity is changing and the car is accelerating.

Types of Acceleration Increasing speed –Example: Car speeds up at green light Decreasing speed –Example: Car slows down at stop light Changing Direction –Example: Car takes turn (can be at constant speed) screeeeech

Acceleration is a vector that points in the same direction as the change in velocity. v0v0 v vv v 0 +  v = v

Acceleration is a vector that points in the same direction as the change in velocity. v0v0 v vv v 0 +  v = v

An object is accelerating when the velocity of the object changes over time. Average acceleration is the the change in velocity  v divided by the change in time  t. –Average acceleration is the slope of the secant line between any two points on a velocity – time graph.

Acceleration is the slope of a velocity – time graph (the derivative of the velocity). Acceleration has a magnitude and a direction and is a vector quantity. Units: m/s 2 (most common); ft/s 2, or km/hr 2.

On a velocity – time graph: –If a is positive, velocity is in the positive direction and the speed of the object is increasing; acceleration is in the positive direction. –The object is increasing its velocity in the positive direction; the object is speeding up and its displacement per unit time is increasing.

On a velocity – time graph: –If a is positive, velocity is in the negative direction and the speed of the object is decreasing; acceleration is in the positive direction. –The object is decreasing its velocity in the negative direction; the object is slowing down and its displacement per unit time is decreasing.

On a velocity – time graph: –If a is negative, velocity is in the positive direction and the speed of the object is decreasing; the acceleration is in the negative direction. –The object is slowing down in the positive direction; the object is slowing down and its displacement per unit time is decreasing.

On a velocity – time graph: –If a is negative, velocity is in the negative direction and the speed of the object is increasing; acceleration is in the negative direction. –The object is speeding up in the negative direction and its displacement per unit time is increasing.

–If a is zero, velocity is constant (not changing); the object could be at rest. The slope of the velocity – time graph is zero (rise = 0). –Three possibilities: –Object at rest: –Constant positive velocity: –Constant negative velocity:

When an object’s velocity and acceleration are in the same direction, the object is speeding up. –Two cases: 1.Positive velocity with positive acceleration: object speeding up in the positive direction. 2.Negative velocity with negative acceleration: object speeding up in the negative direction. When an object’s velocity and acceleration are in opposite directions, the object is slowing down. –Two cases: 1.Positive velocity with negative acceleration: object slowing down in the positive direction. 2.Negative velocity with positive acceleration: object slowing down in the negative direction.

Visualizing Motion with Constant Acceleration Motion diagrams for three carts : An acceleration of 0 m/s 2 tells you the velocity will remain the same each second of the motion. Acceleration tells you the amount by which the velocity will increase (+a) or decrease (-a) each second of the motion.

One-Dimensional Motion with Constant Acceleration Constant or uniform acceleration means that the velocity increases or decreases at the same rate throughout the motion. –The rate of change in the velocity is always the same. Variables to consider: –x i = initial displacement –x f = final displacement –v i = initial velocity –v f = final velocity –a = acceleration –t = time

Velocity as a function of time: Displacement as a function of time:

Velocity as a function of displacement: For motion in which a = 0 m/s 2 (no change in velocity): v i = v f Use the constant velocity equation: Often best to choose x i as 0 m at t = 0 s so that the displacement  x = x f (the final position).

For an object at rest: v i = 0 m/s. For an object that stops: v f = 0 m/s. The term “deceleration” indicates that the acceleration is negative. Examine the known variables before deciding which equation to use to solve the problem. Don’t be too surprised if you have to use one equation to find a variable and then use a second equation to get the desired answer!

If you know the velocity of an object, can you tell me it’s position? –No. An object’s position is independent of the velocity. –You would need to be told the position of the object. If you know the acceleration of an object, can you tell me it’s velocity? –No. An object’s velocity is independent of the acceleration. –You would need to be told the velocity of the object. If you know only the velocity of an object, can you tell me it’s acceleration? –No. An object’s acceleration is the rate of change in velocity, which is independent of the actual velocity at a given instant (the instantaneous velocity). –You would need to know the initial and final velocities of the object to determine the acceleration.

Example: The Aircraft Carrier Jet needs to be traveling 62 m/s for take-off Catapult can accelerate jet up to 31 m/s 2 How long does the carrier have to be?

Example: The Aircraft Carrier What do we know? v i = 0 m/s v f = +62 m/s a = +31 m/s 2 What do we want to know? x = ? Implied data!!

Example: The Aircraft Carrier

Approach to Problem Solving 1.Write down what you know in mathematical terms. (e.g. v 0 =0 m/s) Is there any implied data? 2.Write down what we are trying to figure out (e.g. x=?). 3.Examine the relevant equations and choose the one that will allow us to solve for the quantity in 2) above. 4.Do the algebra!! 5.Plug in the numbers.

What is its final velocity after travelling 215 km? Example: A spacecraft, traveling at m/s fires its reverse thrusters to slow down. The thrusters slow the craft down by 10 m/s every second.

Example: What do we know? v i = m/s a = -10 m/s 2 x = +215 km = +215,000 m What do we want to know? v = ?

Example: