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## Acceleration

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**Acceleration**Acceleration is a vector quantity which is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.**What does acceleration really mean?**• 4.0 m or 4.0 m/s every second s2 Every second the object is increasing its speed 4.0 m s -4.0 m s 2 Every second the object is decreasing its speed by -4.0 m s**Acceleration due to Gravity**There is also gravitational acceleration of -9.8 m/s2 on all objects thrown in the air**Now consider a car moving with a rightward (+), changing**velocity - that is, a car that is moving rightward but speeding up or accelerating**The average acceleration of an object is defined**to be the ratio of its change in velocity to the time taken to change the velocity. v aav = t aav = average acceleration; in units of m/s/s, m/s2 v = change in velocity; in units of m/s, km/hr t = change in time; in units of s, min, hr, etc...**The “sign” of the acceleration**indicates whether the velocity is increasing or decreasing. A positive sign indicates that the velocity is increasing. It will also be an increasein speedif the object is traveling in the positive direction. It is a decrease in speed otherwise. A negative sign indicates that the velocity is decreasing. It will also be a decrease in speedif the object is traveling in the positive direction. It is an increase in speed otherwise.**It is important to note that information about an object’s**acceleration tells us how the object’s velocity is changing. In order to know what this change in velocity is doing to the object’s speed, we must know the direction the object is traveling. As a rule, if the object’s velocity and acceleration are in the same direction (have the same sign), we can say that the object’s speed is increasing. If the velocity and acceleration are in opposite directions (have opposite signs), we know that the object’s speed is decreasing.**1. According to the information above, what is the average**acceleration of the racer in m/s2? Record your answer to the nearest hundredth.**According to the information above, what is the average**acceleration of the racer in m/s2? Record your answer to the nearest hundredth. a = vf – vi = 4.5 m/s – 2.2 m/s = .46 m/s2 tf – ti 5.0s – 0.0 s**2. A rock starts rolling down a hill at**.0194 m/s. One minute later it is rolling at .244 m/s. What is its acceleration?**2. A rock starts rolling down a hill at**.0194 m/s. One minute later it is rolling at .244 m/s. What is its acceleration? a = vf – vi=.244 m/s - .0194 m/s =.00374 m/s2 ∆t 1min 60.s 1min**3. A box accidentally falls from a truck traveling 20.1 m/s**and decelerates at -6.627 m/s2 before it comes to a stop. Find the time it takes it to stop.**3. A box accidentally falls from a truck traveling 20.1 m/s**and decelerates at -6.627 m/s2 before it comes to a stop. Find the time it takes it to stop. a = vf – viso ∆t = vf – vi= 0-20.1m/s ∆t a -6.627 m/s2 ∆t = 3.03 s**4. A rocket starting from rest undergoes an acceleration of**0.60 m/s2 straight upward for 3.0 minutes, when the fuel gives out. What is its final velocity at this point?**4. A rocket starting from rest undergoes an acceleration of**0.600 m/s2 straight upward for 3.00 minutes, when the fuel gives out. What is its final velocity at this point? a = vf – vi so vf – vi = a ∆t ∆tvf = vi + a ∆t vf = 0 m/s + 0.600 m/s2 (3.00 min 60 s) 1 min vf = 108 m/s**Constant Acceleration Equations**• vf = vi + a∆t • a = vf-vi = ∆v tf-ti ∆t • ∆x = vavg ∆t or ∆x = (vf + vi) ∆t 2 • ∆x = vi ∆t + ½ a ∆t**Constant**vf = vi + at t = time x = displacement x = vavt vi = initial velocity vav = (vf + vi)/2 vav = average velocity x = vit + 1/2at2 a = acceleration vf2 = vi2 + 2ax vf = final velocity**Position – Time Graphs Summarized**• the y-coordinate at any time gives the position of the object • the slope of a position-time graph at any instant is the instantaneous • velocity of the object • horizontal graph segments indicate that the object is “at rest” • graph segments moving upward imply movement in the positive • direction • graph segments moving downward imply movement in the negative • direction • straight line graph segments indicate constant speed • curving graph segments indicate changing speed • graph segments becoming steeper indicate an increase in speed • graph segments becoming less steep indicate a decrease in speed • a change of direction is indicated whenever the graph is concave • upward or downward**Velocity – Time Graphs Summarized**• the y-coordinate at any time gives the velocity of the object • the slope of a velocity-time graph is the acceleration of the object • horizontal graph segments indicate that the object has constant • velocity • graph segments above the x-axis imply movement in the positive • direction • graph segments below the x-axis imply movement in the negative • direction • horizontal segments on the x-axis indicate no movement • straight line graph segments indicate constant acceleration • graph segments moving upward indicate an increase in velocity • graph segments moving downward indicate a decrease in velocity • a change of direction is indicated whenever the graph crosses the x- • axis • an increase in speed is indicated by graph segments moving away • from the x-axis**Acceleration – Time Graphs Summarized**• the y-coordinate at any time gives the acceleration of the object • horizontal graph segments indicate that the object has constant • acceleration • a horizontal graph segment on the x-axis indicates that the object • has constant velocity (no acceleration) • graph segments above the x-axis imply increasing velocities • graph segments below the x-axis imply decreasing velocities • no changes in direction may be inferred from these graphs • At the introductory physics level, we typically only deal with constant acceleration situations, so acceleration graphs generally consist of horizontal segments only.