PHY183-Lecture06-3 - 1 Physics for Scientists&Engineers...

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Unformatted text preview: 1 January 18, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 6 Acceleration and Kinematic Equations Acceleration Vector Acceleration Vector The average acceleration is defined as the velocity change per time interval The instantaneous acceleration is given by The acceleration vector is given by January 18, 2012 Physics for Scientists&Engineers 1 2 a x = Δ v x Δ t a x = Δ v x Δ t a x = lim Δ t → a x = lim Δ t → Δ v x Δ t ≡ dv x dt a x = lim Δ t → a x = lim Δ t → Δ v x Δ t ≡ dv x dt a = d v dt a = d v dt Average/Instantaneous Acceleration Average/Instantaneous Acceleration January 18, 2012 Physics for Scientists&Engineers 1 3 Average acceleration over a large time interval Average acceleration over a smaller time interval Instantaneous acceleration at time t 3 January 18, 2012 Physics for Scientists&Engineers 1 4 Example: Velocity & Acceleration Example: Velocity & Acceleration Graph of and Acceleration: v ( t ) = − 10.1 m/s+(2.2 m/s)( t / s) x ( t ) = 17.2 m − (10.1 m)( t / s)+(1.1 m)( t /s) 2 a ( t ) = 2.2 m/s 2 Acceleration Concepts Acceleration Concepts We don’t have a separate word for the absolute value of the acceleration We refer to the deceleration of an object as a decrease in the speed the object over time, which corresponds to acceleration in the opposite direction of the motion of the object If the velocity and acceleration are in the same direction, the object moves faster If the velocity and acceleration are in opposite directions, the object slows down January 18, 2012 Physics for Scientists&Engineers 1 5 Clicker Quiz Clicker Quiz When you’re driving a car along a straight road, you could be traveling in the positive or negative direction and you could have a positive acceleration or a negative acceleration. If you have negative velocity and positive acceleration you are January 18, 2012 Physics for Scientists&Engineers 1 6 A. Slowing down in the positive direction B. Speeding up in the negative direction C. Speeding up in the positive direction D. Slowing down in the negative direction 2 January 18, 2012 Physics for Scientists&Engineers 1 7 Example: 100 m Sprint Example: 100 m Sprint Carl Lewis’ World Record, 1991 World Championship January 18, 2012 Physics for Scientists&Engineers 1 8 Example: 100 m Sprint (2) Example: 100 m Sprint (2) v x = Δ x Δ t Fit: v = 11.6 m/s Fit: v = 11.6 m/s a x = Δ v x Δ t Fit: a = 0.0 m/s Fit: a = 0.0 m/s Displacement and Velocity from Acceleration Displacement and Velocity from Acceleration Integration is the inverse operation to differentiation • Fundamental Theorem of Calculus We can reverse the process we used to get from displacement to velocity to acceleration Why?...
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This note was uploaded on 04/02/2012 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture06-3 - 1 Physics for Scientists&Engineers...

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