Motion in One Dimension Acceleration

What is Acceleration? Acceleration – the rate at which velocity changes over time; an object accelerates if its speed, direction or both change pg44 Physics Serway /Faugh (Holt)

Can an object with constant velocity have an acceleration? Yes, if it changes direction. An object moving in a circle is accelerating. Accelerating objects are objects which are changing their velocity – either the speed (i.e., magnitude of the velocity vector) or the direction. An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards.

Acceleration Examples Many bullet trains have a top speed of about 300 km/h. Because a train stops to load and unload passengers, it does not always travel at that top speed. For some time the train is in motion, its velocity is either increasing or decreasing.

When a shuttle bus approached a stop, the driver begins to apply the brakes to slow down 5.0 s before actually reaching the stop. The speed changes from 9 m/s to 0 m/s over a time interval of 5.0 s. (pg44)

Sometimes, however, the shuttle bus stops much more quickly. For example, if the driver slams on the brakes to avoid hitting a dog, the bus slows from 9 m/s to 0 m/s in just 1.5 s, rather than the 5 s it normally takes. The difference in time intervals for the change in velocity (acceleration) feels very different to the passengers.

Supercollider mean super acceleration (Close to Light Speed =186,000 miles/s) A supercollider is a large ring designed to accelerate particles of protons and anti-protons until they collide, the purpose being to create high amounts of energy.

The Large Hadron Collider (LHC) first started on September 10, 2008, consists of a 27-kilometer ring of superconducting magnets with a number of accelerating structures to boost the energy of the particles along the way. Inside the accelerator, two high-energy particle beams travel at close to the speed of light before they are made to collide.

Acceleration Calculation Acceleration is calculated by dividing the total change in an object’s velocity by the time interval in which the change occurs. (Pg44 Physics Serway/Faughn - Holt)

The SI units of acceleration are meters per second per second, written m/s 2. Meters per second per second (Pg44 Physics Serway/Faughn - Holt)

Acceleration is a Vector Quantity The high-speed train is leaving the station. If the train the is moving to the right, the displacement the and velocity are both +. The velocity increases in magnitude as the train picks speed. (v final >v initial,When  v is +, the acceleration is also +) pg44 Physics Serway /Faugh (Holt) WEST EAST

The train may travel at constant velocity for a while during the journey. (  v & a are both zero.) Finally the train slows so it can eventually stop ( v final <v initial, Whenever is -, the acceleration is - as well)

The Velocity-Time Graph Show Acceleration pg46 Physics Serway /Faugh (Holt )

pg47 Physics Serway /Faugh (Holt)

From: The Physics Classroom.com

Conceptual Challenge #1 (pg 46) pg46 Physics Serway /Faugh (Holt)

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Physics Serway /Faugh (Holt)

Conceptual Challenge #2 (pg 46) Physics Serway /Faugh (Holt)

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Physics Serway /Faugh (Holt)

Conceptual Challenge #3 (pg 46) Physics Serway /Faugh (Holt)

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Physics Serway /Faugh (Holt)

Constant Acceleration During constant acceleration, velocity increases by the same amount during each time interval (  v is the is the same for each similar  t) The successive change in displacements for each time interval increases.

If a ball is dropped, the ball is accelerating at a constant rate. (a due to gravity = 9.81 m/s 2 or 32 ft/s 2 ) Although the change in velocity is the same as each time interval, the displacement increases.

pg46 Physics Serway /Faugh (Holt)

Graphing Comparisons Graphing Comparisons Position-Time, Velocity-Time, Acceleration-Time Physics Flash Animations

The slope of Position-Time graph can be used to produce the Velocity-Time graph

The slope of the Velocity-Time graph can be used to produce the Acceleration-Time graph.

Position-Time, Velocity-Time, Acceleration-Time

The area of the acceleration-time graph can be used to produce the velocity time graph.

Position-Time, Velocity-Time, Acceleration-Time