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Example 2.3 Average and Instantaneous Velocity x (m) 10 particle moves along the x axis. Its position varies with me according to the expression x = -4t + 27, where x is a meters and t is in seconds. The position-time graph for mis motion is shown in the figure. Notice that the particle oves in the negative x direction for the first second of otion, is momentarily at rest at the moment t = oves in the positive x direction at times t > 1 s. 8 Slope +4 m/s 6. %3D 1 s, and Slope -2 m/s 2 ) Determine the displacement of the particle in the time tervals t = 0 to t 1 s andt = 1 s to t = 3 s. %3D -2 O Calculate the average velocity during these two time cervals. 4 1 Find the instantaneous velocity of the particle at t = 5 s. SOLVE IT Determine the displacement of the particle in the time intervals = 0 to t = 1 s and z = 1 s to t m the graph, form a mental representation of the motion of the particle. Keep in mind that the ticle does not move in a curved path in space such as that shown by the brown curve in the phical representation. The particle moves only along the x axis in one dimension. At r = 0, is it ving to the right or to the left? ing the first time interval, the slope is negative and hence the average velocity is negative. -efore, we know that the displacement between O and must be a negative number having s of meters. Similarly, we expect the displacement between and to be positive. ne first time interval, set i = , = 0 and E = 1s and use the following equation Ax = x,- x = XX Ax =[-4(1) + 2(1) 1-[-4(0) + 2(0) 1 %3! nd the displacement: e second time interval (: = 1 s to z = %3D x-Ox = x- x = -x 2. 4.

Example 2.3 Average and Instantaneous Velocity x (m) 10 particle moves along the x axis. Its position varies with me according to the expression x = -4t + 27, where x is a meters and t is in seconds. The position-time graph for mis motion is shown in the figure. Notice that the particle oves in the negative x direction for the first second of otion, is momentarily at rest at the moment t = oves in the positive x direction at times t > 1 s. 8 Slope +4 m/s 6. %3D 1 s, and Slope -2 m/s 2 ) Determine the displacement of the particle in the time tervals t = 0 to t 1 s andt = 1 s to t = 3 s. %3D -2 O Calculate the average velocity during these two time cervals. 4 1 Find the instantaneous velocity of the particle at t = 5 s. SOLVE IT Determine the displacement of the particle in the time intervals = 0 to t = 1 s and z = 1 s to t m the graph, form a mental representation of the motion of the particle. Keep in mind that the ticle does not move in a curved path in space such as that shown by the brown curve in the phical representation. The particle moves only along the x axis in one dimension. At r = 0, is it ving to the right or to the left? ing the first time interval, the slope is negative and hence the average velocity is negative. -efore, we know that the displacement between O and must be a negative number having s of meters. Similarly, we expect the displacement between and to be positive. ne first time interval, set i = , = 0 and E = 1s and use the following equation Ax = x,- x = XX Ax =[-4(1) + 2(1) 1-[-4(0) + 2(0) 1 %3! nd the displacement: e second time interval (: = 1 s to z = %3D x-Ox = x- x = -x 2. 4.

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A webassign.net/web/Student/Assignment-Responses/last?dep326272405 : Apps M Gmail Maps YouTube Translate Microsoft Office Ho... Check Y. Example 2.3 Average and Instantaneous Velocity x (m) 10 A particle moves along the x axis. Its position varies with time according to the expression x = -4t + 2r, where x is in meters and t is in seconds. The position-time graph for this motion is shown in the figure. Notice that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment t = 1 s, and moves in the positive x direction at times t > 1 s. 8 Slope = +4 m/s 6 Slope = -2 m/s 4 (A) Determine the displacement of the particle in the time 0. t (s) intervals t= 0 to t = 1 s and t = 1 s to t = 3 s. B (B) Calculate the average velocity during these two time intervals. 4 (C) Find the instantaneous velocity of the particle at t = 2.5 s. SOLVE IT (A) Determine the displacement of the particle in the time intervals = 0 tot = 1 s and z = 1 s to t = 3 s. From the graph, form a mental representation of the motion of the particle. Keep in mind that the particle does not move in a curved path in space such as that shown by the brown curve in the graphical representation. The particle moves only along the x axis in one dimension. At r = 0, is it moving to the right or to the left? During the first time interval, the slope is negative and hence the average velocity is negative. Therefore, we know that the displacement between and (B) must be a negative number having units of meters. Similarly, we expect the displacement between and to be positive. In the first time interval, set i = 1, = 0 and x- x = x .*x = "-"xp Ax = [ -4(1) + 2(1) ]- [-4(0) + 2(0)1 1, = = 1s and use the follovwing equation to find the displacement: Ar. For the second time interval (1 = 1 s to = W
Transcribed Image Text:A webassign.net/web/Student/Assignment-Responses/last?dep326272405 : Apps M Gmail Maps YouTube Translate Microsoft Office Ho... Check Y. Example 2.3 Average and Instantaneous Velocity x (m) 10 A particle moves along the x axis. Its position varies with time according to the expression x = -4t + 2r, where x is in meters and t is in seconds. The position-time graph for this motion is shown in the figure. Notice that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment t = 1 s, and moves in the positive x direction at times t > 1 s. 8 Slope = +4 m/s 6 Slope = -2 m/s 4 (A) Determine the displacement of the particle in the time 0. t (s) intervals t= 0 to t = 1 s and t = 1 s to t = 3 s. B (B) Calculate the average velocity during these two time intervals. 4 (C) Find the instantaneous velocity of the particle at t = 2.5 s. SOLVE IT (A) Determine the displacement of the particle in the time intervals = 0 tot = 1 s and z = 1 s to t = 3 s. From the graph, form a mental representation of the motion of the particle. Keep in mind that the particle does not move in a curved path in space such as that shown by the brown curve in the graphical representation. The particle moves only along the x axis in one dimension. At r = 0, is it moving to the right or to the left? During the first time interval, the slope is negative and hence the average velocity is negative. Therefore, we know that the displacement between and (B) must be a negative number having units of meters. Similarly, we expect the displacement between and to be positive. In the first time interval, set i = 1, = 0 and x- x = x .*x = "-"xp Ax = [ -4(1) + 2(1) ]- [-4(0) + 2(0)1 1, = = 1s and use the follovwing equation to find the displacement: Ar. For the second time interval (1 = 1 s to = W
DYC A webassign.net/web/Student/Assignment-Responses/last?dep=26272405 : Apps M Gmail Maps O YouTube Translate Microsoft Office Ho... Check Your P For the second time interval (t = 1s to t = Bx _ Ox = 'x - hx = a-exy Axp = [ -4(3) + 2(3)² ] - [ -4(1) + 2(1)² ] Axg¬p = 3 s), set 4 = t = 1 s and t4 = t, = 3 s: These displacements can also be read directly from the position-time graph. (B) Calculate the average velocity during these two time intervals. In the first time interval, use the equation for average velocity with Axt = t4 - = tg - Axa-8 -2 m Vx, avg (A -B)= Axt 1s tA = 1 s: Vx, avg (A -B) = m/s In the second time interval, Axt = 2 s: 8 m 2 s Vx, avg (8 -D)= Axt V, avg (8 -D) = m/s These values are the same as the slopes of the lines joining these points in the figure. (C) Find the instantaneous velocity of the particle at t = 2.5 s. Measure the slope of the green line at z = v = 2.5 s (point C) in the figure: m/s Notice that this instantaneous velocity is on the same order of magnitude as our previous results, that is, a few m MASTER IT HINTS: GETTING STARTED | I'M STUCK! Suppose a particle moves along the x axis. Its x coordinate varies with time according to the expression x = 30 + 3.3r + 2.3r, where x is in meters andt is in seconds. (a)Determine the displacement Ax of the particle in the time interval : = 9 s to r = 20 s. Ax = (b) Calculate the average velocity in the time interval: = 9 s to = 20 s. m/s (c) Find the instantaneous velocity of the particle at : = 18,4 s. m/s
Transcribed Image Text:DYC A webassign.net/web/Student/Assignment-Responses/last?dep=26272405 : Apps M Gmail Maps O YouTube Translate Microsoft Office Ho... Check Your P For the second time interval (t = 1s to t = Bx _ Ox = 'x - hx = a-exy Axp = [ -4(3) + 2(3)² ] - [ -4(1) + 2(1)² ] Axg¬p = 3 s), set 4 = t = 1 s and t4 = t, = 3 s: These displacements can also be read directly from the position-time graph. (B) Calculate the average velocity during these two time intervals. In the first time interval, use the equation for average velocity with Axt = t4 - = tg - Axa-8 -2 m Vx, avg (A -B)= Axt 1s tA = 1 s: Vx, avg (A -B) = m/s In the second time interval, Axt = 2 s: 8 m 2 s Vx, avg (8 -D)= Axt V, avg (8 -D) = m/s These values are the same as the slopes of the lines joining these points in the figure. (C) Find the instantaneous velocity of the particle at t = 2.5 s. Measure the slope of the green line at z = v = 2.5 s (point C) in the figure: m/s Notice that this instantaneous velocity is on the same order of magnitude as our previous results, that is, a few m MASTER IT HINTS: GETTING STARTED | I'M STUCK! Suppose a particle moves along the x axis. Its x coordinate varies with time according to the expression x = 30 + 3.3r + 2.3r, where x is in meters andt is in seconds. (a)Determine the displacement Ax of the particle in the time interval : = 9 s to r = 20 s. Ax = (b) Calculate the average velocity in the time interval: = 9 s to = 20 s. m/s (c) Find the instantaneous velocity of the particle at : = 18,4 s. m/s
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