Motion in One Dimension – PART 2

Motion Diagrams An object starts from rest and moves with constant acceleration. 4 8 12 16 20 24 28 (s) x 4 8 12 16 20 24 28 (m) 1 2 3 t 5

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

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

(s) x 4 8 12 16 20 24 28 (m) 1 2 3 t 5 Motion Diagrams 1 2 3 4 5 t (s) 6 8 10 v (m/s) Displacement 25 m

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

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

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

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

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

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 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

One Dimensional Motion with Constant Acceleration For constant acceleration An object moving with a velocity vo is passing position xo when it undergoes a constant acceleration a for a time t. Find the object’s displacement. time = 0 time = t xo ? a vo Solution: Eq 2

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

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

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

One Dimensional Motion with Constant Acceleration 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.

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.

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/s2. (a) How long does it take for the lead car to stop?

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/s2. (b) How far does the lead car travel during the acceleration?

Problem Alternate Solutions

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/s2. (c) Assuming that the chasing car brakes at the same time as the lead car, what must be the chasing car’s minimum negative acceleration so as not to hit the lead car?

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/s2. (d) How long does it take for the chasing car to stop?

Problem Alternate Solutions

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

Problem A drag racer starts her car from rest and accelerates at 10.0 m/s2 for a distance of 400 m (1/4 mile). (a) How long did it take the race car to travel this distance?

Problem A drag racer starts her car from rest and accelerates at 10.0 m/s2 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 A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise?

Problem 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 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 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?

Review Definitions Average velocity Average acceleration Kinematics with Constant Acceleration

Review t x v a t x v a Dt Dv Dx

Problem Solving Skills Review 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 Kinematics in One Dimension (Phy 2053) vittitoe

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Constant Velocity 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.

Freely Falling Objects 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 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 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.