Average and Instantaneous Acceleration The velocity of a particle moving along the x-axis varies according to the expression x = (55 - 0.6t2) m/s, where vx is in meters per second and t is in seconds. v, (m/s) B 0 1 2 3 t(s) The velocity-time graph for a particle moving along the x-axis. (b) Determine the acceleration at t -2.0 s. SOLUTION (Use the following as necessary: t and At.) Knowing that the initial velocity at any time t is vi- (55 -0.02) m/s, find the velocity at any later time t + At: m/s Find the change in velocity over the time interval At: Ax m/s To find the acceleration at any time, divide this expression by At and take the limit of the result as At approaches zero: Av. - lim at-0 m/s² Substitute -2.0 s (Enter your answer in m/s. Indicate the direction with the sign of your answer.): Because the velocity of the particle is positive and the acceleration is negative at this instant, the particle is Blowing down ✔✔ Notice that the answers to parts (a) and (b) are different. The average acceleration in (a) is the slope of the blue line in the figure above connecting points A and B. The instantaneous acceleration in (b) is the slope of the green line tangent to the curve at point B. Notice also that the acceleration is not constant in this example. Situations involving constant acceleration are treated later. EXERCISE Suppose the velocity of a particle moving along the x-axis varies in time according to the expression vx-(4.9 +1.60 +7.5t2] where t is in seconds. Hint (a) Find the average acceleration (in m/s²) in the time interval - 5.1 s to -6.3 s. (Indicate the direction with the sign of your answer.) m² (b) Determine the acceleration (in m/s²) at -8.7 s. (Indicate the direction with the sign of your answer.) m/s²
Average and Instantaneous Acceleration The velocity of a particle moving along the x-axis varies according to the expression x = (55 - 0.6t2) m/s, where vx is in meters per second and t is in seconds. v, (m/s) B 0 1 2 3 t(s) The velocity-time graph for a particle moving along the x-axis. (b) Determine the acceleration at t -2.0 s. SOLUTION (Use the following as necessary: t and At.) Knowing that the initial velocity at any time t is vi- (55 -0.02) m/s, find the velocity at any later time t + At: m/s Find the change in velocity over the time interval At: Ax m/s To find the acceleration at any time, divide this expression by At and take the limit of the result as At approaches zero: Av. - lim at-0 m/s² Substitute -2.0 s (Enter your answer in m/s. Indicate the direction with the sign of your answer.): Because the velocity of the particle is positive and the acceleration is negative at this instant, the particle is Blowing down ✔✔ Notice that the answers to parts (a) and (b) are different. The average acceleration in (a) is the slope of the blue line in the figure above connecting points A and B. The instantaneous acceleration in (b) is the slope of the green line tangent to the curve at point B. Notice also that the acceleration is not constant in this example. Situations involving constant acceleration are treated later. EXERCISE Suppose the velocity of a particle moving along the x-axis varies in time according to the expression vx-(4.9 +1.60 +7.5t2] where t is in seconds. Hint (a) Find the average acceleration (in m/s²) in the time interval - 5.1 s to -6.3 s. (Indicate the direction with the sign of your answer.) m² (b) Determine the acceleration (in m/s²) at -8.7 s. (Indicate the direction with the sign of your answer.) m/s²
An Introduction to Physical Science
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ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
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Chapter1: Measurement
Section: Chapter Questions
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![Average and Instantaneous Acceleration
The velocity of a particle moving along the x-axis varies according to the expression x = (55 - 0.6t2) m/s, where vx is in meters per second and t is in seconds.
v, (m/s)
B
0
1
2
3
t(s)
The velocity-time graph for a particle
moving along the x-axis.
(b) Determine the acceleration at t -2.0 s.
SOLUTION
(Use the following as necessary: t and At.)
Knowing that the initial velocity at any time t is vi- (55 -0.02) m/s, find the velocity at any later time t + At:
m/s
Find the change in velocity over the time interval At:
Ax
m/s
To find the acceleration at any time, divide this expression by At and take the limit of the result as At approaches zero:
Av.
- lim
at-0
m/s²
Substitute -2.0 s (Enter your answer in m/s. Indicate the direction with the sign of your answer.):
Because the velocity of the particle is positive
and the acceleration is negative
at this instant, the particle is Blowing down ✔✔
Notice that the answers to parts (a) and (b) are different. The average acceleration in (a) is the slope of the blue line in the figure above connecting points A and B. The instantaneous acceleration in (b) is the slope of the green line tangent to the curve at point B. Notice also that the acceleration is not
constant in this example. Situations involving constant acceleration are treated later.
EXERCISE
Suppose the velocity of a particle moving along the x-axis varies in time according to the expression vx-(4.9 +1.60 +7.5t2] where t is in seconds.
Hint
(a) Find the average acceleration (in m/s²) in the time interval - 5.1 s to -6.3 s. (Indicate the direction with the sign of your answer.)
m²
(b) Determine the acceleration (in m/s²) at -8.7 s. (Indicate the direction with the sign of your answer.)
m/s²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde27a534-4354-44e2-a5fc-ba27a8349552%2F4f5f5bf6-99be-448b-a54a-594045fc581f%2F0c0kgzl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Average and Instantaneous Acceleration
The velocity of a particle moving along the x-axis varies according to the expression x = (55 - 0.6t2) m/s, where vx is in meters per second and t is in seconds.
v, (m/s)
B
0
1
2
3
t(s)
The velocity-time graph for a particle
moving along the x-axis.
(b) Determine the acceleration at t -2.0 s.
SOLUTION
(Use the following as necessary: t and At.)
Knowing that the initial velocity at any time t is vi- (55 -0.02) m/s, find the velocity at any later time t + At:
m/s
Find the change in velocity over the time interval At:
Ax
m/s
To find the acceleration at any time, divide this expression by At and take the limit of the result as At approaches zero:
Av.
- lim
at-0
m/s²
Substitute -2.0 s (Enter your answer in m/s. Indicate the direction with the sign of your answer.):
Because the velocity of the particle is positive
and the acceleration is negative
at this instant, the particle is Blowing down ✔✔
Notice that the answers to parts (a) and (b) are different. The average acceleration in (a) is the slope of the blue line in the figure above connecting points A and B. The instantaneous acceleration in (b) is the slope of the green line tangent to the curve at point B. Notice also that the acceleration is not
constant in this example. Situations involving constant acceleration are treated later.
EXERCISE
Suppose the velocity of a particle moving along the x-axis varies in time according to the expression vx-(4.9 +1.60 +7.5t2] where t is in seconds.
Hint
(a) Find the average acceleration (in m/s²) in the time interval - 5.1 s to -6.3 s. (Indicate the direction with the sign of your answer.)
m²
(b) Determine the acceleration (in m/s²) at -8.7 s. (Indicate the direction with the sign of your answer.)
m/s²
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