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x. dx. t. dt. Motion in One Dimension. Physics 2053 Lecture Notes. Motion in One Dimension (2053). . Motion in 1 Dimension. v. In the study of kinematics, we consider a moving object as a particle. A particle is a point-like mass having infinitesimal size and a finite mass.

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## Motion in One Dimension

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**x**dx t dt Motion in One Dimension Physics 2053 Lecture Notes Motion in One Dimension (2053)****Motion in 1 Dimension v In the study of kinematics, we consider a moving object as a particle. A particle is a point-like mass having infinitesimal size and a finite mass. Motion in One Dimension (2053)**Dx = x - xo**= 6 m - 2 m = 4 m Motion in 1 Dimension Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Note:Motion to the right is positive Motion in One Dimension (2053)**Dx = x - xo**= -6 m - 6 m = -12 m Motion in 1 Dimension Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Note:Motion to the left is negative Motion in One Dimension (2053)**Dx = x - xo**= (2 m) - (-6 m) = 8 m Motion in 1 Dimension Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Note:Motion to the right is positive Motion in One Dimension (2053)**x2**Dx x1 Dt t1 t2 Motion in 1 Dimension Average velocity The average velocity of a particle is defined as x Velocity is represented by the slope on a displacement-time graph t Motion in One Dimension (2053)**Motion in 1 Dimension**Average speed The average speed of a particle is defined as Motion in One Dimension (2053)**x**Dx t Dt Motion in 1 Dimension Instantaneous velocity The instantaneous velocity v, equals the limiting value of the ratio Instantaneous velocity is represented by the slope of a displacement-time graph Motion in One Dimension (2053)**Motion in 1 Dimension**Instantaneous speed The instantaneous speed of a particle is defined as the magnitude of its instantaneous velocity. Motion in One Dimension (2053)**v2**Dv v1 Dt t1 t2 Motion in 1 Dimension Average acceleration The average acceleration of a particle is defined as the change in velocity Dvx divided by the time interval Dt during which that change occurred. v Acceleration is represented by the slope on a velocity-time graph t Motion in One Dimension (2053)**v**Dv t Dt Motion in 1 Dimension Instantaneous acceleration The instantaneous acceleration equals the derivative of the velocity with respect to time Instantaneous acceleration is represented by the slope of a velocity-time graph Motion in One Dimension (2053)**The slope of a displacement-time**graph represents velocity The slope of a velocity-time graph represents acceleration Motion in 1 Dimension Displacement, velocity and acceleration graphs x t v t a t Motion in One Dimension (2053)**Dx**The area under a velocity-time graph represents displacement. Dv The area under an acceleration-time graph represents change in velocity. Motion in 1 Dimension Displacement, velocity and acceleration graphs x t v t a Dt t Motion in One Dimension (2053)**Average velocity**Average acceleration Motion in 1 Dimension Definitions of velocity and acceleration Motion in One Dimension (2053)**Motion in 1 Dimension**For constant acceleration An object moving with an initial velocity voundergoes a constant acceleration a for a time t. Find the final velocity. vo ? a time = 0 time = t Solution: Eq 1 Motion in One Dimension (2053)**a**t 0 What are we calculating? DV Motion in One Dimension (2053)**time = 0**time = t a vo ? xo Eq 2 Motion in 1 Dimension For constant acceleration An object moving with a velocity vo is passing position xowhen itundergoes a constant acceleration a for a time t. Find the object’s final position. Solution: Motion in One Dimension (2053)**v**at vi 0 t What are we calculating? Motion in One Dimension (2053)**Eq 1**Eq 2 Eq 3 Eq 4 Motion in 1 Dimension Solve Eq 1 for a and sub into Eq 2: Solve Eq 1 for t and sub into Eq 2: Motion in One Dimension (2053)**Motion in 1 Dimension**Problem 2-3 The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s Motion in One Dimension (2053)**Motion in 1 Dimension**Problem 2-3 The displacement versus time for a certain particle moving along the x axis is shown in Figure P2.3. Find the average velocity in the time intervals (b) 0 to 4 s Motion in One Dimension (2053)**Motion in 1 Dimension**Problem 2-3 The displacement versus time for a certain particle moving along the x axis is shown in Figure P2.3. Find the average velocity in the time intervals (d) 4 s to 7 s Motion in One Dimension (2053)**Motion in 1 Dimension**More Graphs Motion in One Dimension (2053)**-6**-5 -4 -3 -2 -1 0 1 1 2 3 4 5 6 Motion in One Dimension (2053)**-6**-5 -4 -3 -2 -1 0 1 1 2 3 4 5 6 Motion in One Dimension (2053)**-6**-5 -4 -3 -2 -1 0 1 1 2 3 4 5 6 Motion in One Dimension (2053)**6**5 4 3 2 1 1 0 2 4 6 8 10 12 -1 -2 -3 -4 -5 -6 Motion in One Dimension (2053)**6**5 4 3 2 1 1 0 2 4 6 8 10 12 -1 -2 -3 -4 -5 -6 Motion in One Dimension (2053)**6**5 4 3 2 1 1 0 2 4 6 8 10 12 -1 -2 -3 -4 -5 -6 Motion in One Dimension (2053)**6**m 5 4 3 2 1 1 0 2 4 6 8 10 12 -1 s -2 -3 -4 -5 -6 Motion in One Dimension (2053)**6**m 4 2 0 2 4 6 8 10 12 s -2 -4 -6 2 v 1 0 t 4 8 12 (s) -1 (m/s) -2 -3 Motion in One Dimension (2053)**6**m 4 2 0 2 4 6 8 10 12 s -2 -4 -6 2 v +8 m 1 +4 m 0 t 4 8 12 (s) -1 (m/s) -12 m -2 -3 Motion in One Dimension (2053)**28**x 24 20 16 (m) 12 8 4 t 1 2 3 4 5 (s) 0 4 8 12 16 20 24 28 Motion in One Dimension (2053)**28**x 24 10 20 v 8 16 (m) 12 6 (m/s) 8 4 2 4 Displacement 25 m t 1 2 3 4 5 1 2 3 4 5 t (s) (s) Motion in One Dimension (2053)**Average velocity**Average acceleration Review: Definitions Kinematics with Constant Acceleration Motion in One Dimension (2053)**x**x Dx t t v v Dv t t a a t Dt t Review: Motion in One Dimension (2053)**Problem Solving Skills**1. Read the problem carefully 2. Sketch the problem 3. Visualize the physical situation 4. Strategize 5. Identify appropriate equations 6. Solve the equations 7. Check your answers Motion in One Dimension (2053)

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