Lecture: Acceleration A vector quantity CCHS Physics.

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Presentation transcript:

Lecture: Acceleration A vector quantity CCHS Physics

Acceleration The rate of change in velocity We can change the velocity of an object by: –changing its speed –changing its direction –(or changing both)

Meaning of Acceleration In everyday language ‘acceleration’ refers to a gain in speed and ‘deceleration’ to a decrease in speed. In physics we will speak only of acceleration, and we will define it as being either positive or negative. Acceleration is positive when the change in velocity is positive and negative when the change in velocity is negative. True or false? If your speed is increasing, you must have a positive acceleration.

ANSWER False! To increase speed in positive direction = positive acceleration but an increase in speed in the negative direction = negative acceleration

Acceleration Video

Reminders Velocity is the rate of change of position. It can be found graphically by taking the slope of a position vs. time graph. Acceleration is the rate of change of velocity. It can be found graphically by taking the slope of a velocity vs. time graph.

Let’s try some examples… A car starts from rest and accelerates uniformly at 3 m/s 2 north. What is its velocity after 5 seconds? A bus traveling west at 20 m/s slows uniformly to 8 m/s in 6 seconds. What is its acceleration?

Acceleration Graphing Movie

Try this one… During which of the following intervals is the acceleration the greatest: t = s t = s t = s Ha ha that was a trick. It’s zero everywhere. How would a position vs. time graph look like if an object was accelerating?

Let’s Add in Some Calc! Instantaneous Acceleration Relating back to position: So, acceleration is the second derivative of position with respect to time

Calc Example If the velocity of dog is given by the equation v(t) = 5t + 1, what is the acceleration of the dog at 4 s? If the position of a bee is given by the equation x(t) =.6t 2 + 3t + 1, what is the acceleration of the snail at 7 s?

“What about Integrals?” - Integral Man So, remember that derivatives and integrals and opposites: EXAMPLE: If the acceleration of a bus is given by a(t) = 2t, what is the velocity after 4 s if the initial velocity is 7 m/s? –We’ve got to solve for C using initial conditions