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Motion in One Dimension – PART 2

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(s) x (m) 1234 t 5 Motion Diagrams An object starts from rest and moves with constant acceleration.

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t x t v t a Displacement, velocity and acceleration graphs The slope of a velocity-time graph represents acceleration The slope of a displacement-time graph represents velocity Motion Diagrams Kinematics in One Dimension (Phy 2053) vittitoe

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t x t v t a t Displacement, velocity and acceleration graphs The area under an acceleration-time graph represents change in velocity. v The area under a velocity-time graph represents displacement. x Motion Diagrams Kinematics in One Dimension (Phy 2053) vittitoe

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(s) x (m) 1234 t t (s) v (m/s) Displacement 25 m Motion Diagrams

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Kinematics in One Dimension (Phy 2053) vittitoe The slope of a position versus time graph gives A) position. B) velocity. C) acceleration. D) displacement.

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Motion Diagrams Kinematics in One Dimension (Phy 2053) vittitoe The slope of a velocity versus time graph gives A) position. B) velocity C) acceleration D) displacement

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Definitions of velocity and acceleration Average velocity Average acceleration One Dimensional Motion with Constant Acceleration Kinematics in One Dimension (Phy 2053) vittitoe

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For constant acceleration An object moving with an initial velocity v o undergoes a constant acceleration a for a time t. Find the final velocity. vovo time = 0time = t Solution: Eq 1 a ? One Dimensional Motion with Constant Acceleration Kinematics in One Dimension (Phy 2053) vittitoe

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What are we calculating? 0 t a V One Dimensional Motion with Constant Acceleration

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Objects A and B both start at rest. They both accelerate at the same rate. However, object B accelerates for twice the time as object A. What is the final speed of object B compared to that of object A? A) the same speed B) twice as fast C) three times as fast D) four times as fast

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For constant acceleration An object moving with a velocity v o is passing position x o when it undergoes a constant acceleration a for a time t. Find the objects displacement. Solution: time = 0time = t xoxo ? a vovo Eq 2 One Dimensional Motion with Constant Acceleration

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What are we calculating? 0 t vovo v One Dimensional Motion with Constant Acceleration at

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One Dimensional Motion with Constant Acceleration Objects A and B both start at rest. They both accelerate at the same rate. However, object B accelerates for twice the time as object A. What is the distance traveled by object B compared to that of object A? A) the same distance B) twice as far C) three times as far D) four times as far

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Eq 1 Eq 2 Solve Eq 1 for a and sub into Eq 2: Solve Eq 1 for t and sub into Eq 2: Eq 3 Eq 4 One Dimensional Motion with Constant Acceleration

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When the velocity of an object is zero, must its acceleration also be zero? A) no, an object thrown upward will have zero velocity at its highest point. B) no, a falling object will have zero velocity after hitting the ground. C) yes, if the object is not moving it can not be accelerating. D) yes, acceleration implies a changing velocity, it can not be zero.

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Freely Falling Objects When an object is released from rest and falls in the absence of air resistance, which of the following is true concerning its motion? A) Its acceleration is constant B) Its velocity is constant. C) Neither its acceleration nor its velocity is constant. D) Both its acceleration and its velocity are constant.

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Problem Two cars are traveling along a straight line in the same direction, the lead car at 25.0 m/s and the other car at 30.0 m/s. At the moment the cars are 40.0 m apart, the lead driver applies the brakes, causing his car to have an acceleration of –2.00 m/s 2. (a) How long does it take for the lead car to stop?

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Problem Two cars are traveling along a straight line in the same direction, the lead car at 25.0 m/s and the other car at 30.0 m/s. At the moment the cars are 40.0 m apart, the lead driver applies the brakes, causing his car to have an acceleration of –2.00 m/s 2. (b) How far does the lead car travel during the acceleration?

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Alternate Solutions Problem

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Two cars are traveling along a straight line in the same direction, the lead car at 25.0 m/s and the other car at 30.0 m/s. At the moment the cars are 40.0 m apart, the lead driver applies the brakes, causing his car to have an acceleration of –2.00 m/s 2. (c) Assuming that the chasing car brakes at the same time as the lead car, what must be the chasing cars minimum negative acceleration so as not to hit the lead car?

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Two cars are traveling along a straight line in the same direction, the lead car at 25.0 m/s and the other car at 30.0 m/s. At the moment the cars are 40.0 m apart, the lead driver applies the brakes, causing his car to have an acceleration of –2.00 m/s2. (d) How long does it take for the chasing car to stop? Problem

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Alternate Solutions Problem

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A Cessna aircraft has a lift-off speed of 120 km/h. (a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240 m? Problem

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A Cessna aircraft has a lift-off speed of 120 km/h. (b) How long does it take the aircraft to become airborne? Problem

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A drag racer starts her car from rest and accelerates at 10.0 m/s 2 for a distance of 400 m (1/4 mile). (a) How long did it take the race car to travel this distance? Problem

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A drag racer starts her car from rest and accelerates at 10.0 m/s 2 for a distance of 400 m (1/4 mile). (b) What is the speed of the race car at the end of the run? Problem

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A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? Problem

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A ball is thrown vertically upward with a speed of 25.0 m/s. (b) How long does it take to reach its highest point? Problem

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A ball is thrown vertically upward with a speed of 25.0 m/s. (c) How long does the ball take to hit the ground after it reaches its highest point? Problem

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A ball is thrown vertically upward with a speed of 25.0 m/s. (d) What is its velocity when it returns to the level from which it started? Problem

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Average velocity Average acceleration Kinematics with Constant Acceleration Definitions Review

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t x t v t a t v x t x t v t a

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Problem Solving Skills 1. Read the problem carefully 2. Sketch the problem 3. Visualize the physical situation 4. Identify the known and unknown quantities 5. Identify appropriate equations 6. Solve the equations 7. Check your answers Review Kinematics in One Dimension (Phy 2053) vittitoe

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Suppose that an object is moving with a constant velocity. Make a statement concerning its acceleration. A) The acceleration must be constantly increasing. B) The acceleration must be constantly decreasing. C) The acceleration must be a constant non-zero value. D) The acceleration must be equal to zero. Constant Velocity

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Can an object have increasing speed while the magnitude of its acceleration is decreasing? Support your answer with an example. A) No, this is impossible because of the way in which acceleration is defined. B) No, because if acceleration is decreasing the object will be slowing down. C) Yes, and an example would be an object falling in the absence of air friction. D) Yes, and an example would be an object released from rest in the presence of air friction. Freely Falling Objects

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Suppose a ball is thrown straight up. Make a statement about the velocity and the acceleration when the ball reaches the highest point. A) Both its velocity and its acceleration are zero. B) Its velocity is zero and its acceleration is not zero. C) Its velocity is not zero and its acceleration is zero. D) Neither its velocity nor its acceleration is zero. Freely Falling Objects

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Ball A is dropped from the top of a building. One second later, ball B is dropped from the same building. As time progresses, the distance between them A) increases. B) remains constant. C) decreases. D) cannot be determined from the information given. Freely Falling Objects

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