Podcast
Questions and Answers
If the velocity of a particle is nonzero, can its acceleration be zero? Explain.
If the velocity of a particle is nonzero, can its acceleration be zero? Explain.
Yes. If the velocity of the particle is nonzero, the particle is in motion. If the acceleration is zero, the velocity of the particle is unchanging, or is a constant.
If the velocity of a particle is zero, can its acceleration be nonzero? Explain.
If the velocity of a particle is zero, can its acceleration be nonzero? Explain.
Yes. If you drop a doughnut from rest (v = 0), then its acceleration is not zero. A common misconception is that immediately after the doughnut is released, both the velocity and acceleration are zero. If the acceleration were zero, then the velocity would not change, leaving the doughnut floating at rest in mid-air.
Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of car A exceeds the velocity of car B. This means that the acceleration of A is greater than that of B.
Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of car A exceeds the velocity of car B. This means that the acceleration of A is greater than that of B.
False (B)
Secretariat won the Kentucky Derby with times for successive quarter-mile segments of 25.2 s, 24.0 s, 23.8 s, and 23.0. Find his average speed during each quarter-mile segment.
Secretariat won the Kentucky Derby with times for successive quarter-mile segments of 25.2 s, 24.0 s, 23.8 s, and 23.0. Find his average speed during each quarter-mile segment.
Assuming that Secretariat's instantaneous speed at the finish line was the same as the average speed during the final quarter mile, find his average acceleration for the entire race. (Horses in the Derby start from rest.)
Assuming that Secretariat's instantaneous speed at the finish line was the same as the average speed during the final quarter mile, find his average acceleration for the entire race. (Horses in the Derby start from rest.)
Draw motion diagrams for the following: (a) an object moving to the right at a constant speed, (b) an object moving to the right and speeding up at a constant rate (c) an object moving to the right and slowing down at a constant rate, (d) an object moving to the left and speeding up at a constant rate, and (e) an object moving to the left and slowing down at a constant rate.
Draw motion diagrams for the following: (a) an object moving to the right at a constant speed, (b) an object moving to the right and speeding up at a constant rate (c) an object moving to the right and slowing down at a constant rate, (d) an object moving to the left and speeding up at a constant rate, and (e) an object moving to the left and slowing down at a constant rate.
How would your drawings change if the changes in speed were not uniform, that is, if the speed were not changing at a constant rate?
How would your drawings change if the changes in speed were not uniform, that is, if the speed were not changing at a constant rate?
The position versus time for a certain particle moving along the x-axis is shown. Find the average velocity in the time intervals: (a) 0 to 2s, (b) 0 to 4s, (c) 2 s to 4 s, (d) 4 s to 7s, (e) 0 to 8 s.
The position versus time for a certain particle moving along the x-axis is shown. Find the average velocity in the time intervals: (a) 0 to 2s, (b) 0 to 4s, (c) 2 s to 4 s, (d) 4 s to 7s, (e) 0 to 8 s.
A person walks first at a constant speed of 5.00 m/s along a straight line from point A to point B and then back along the line from B to A at a constant speed of 3.00 m/s. What is (a) her average speed over the entire trip? (b) her average velocity over the entire trip?
A person walks first at a constant speed of 5.00 m/s along a straight line from point A to point B and then back along the line from B to A at a constant speed of 3.00 m/s. What is (a) her average speed over the entire trip? (b) her average velocity over the entire trip?
The position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds. Evaluate its position (a) at t = 3.00 s and (b) at 3.00 s + Δt. (c) Evaluate the limit of Δx/Δt as Δt approaches zero, to find the velocity at t = 3.00 s.
The position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds. Evaluate its position (a) at t = 3.00 s and (b) at 3.00 s + Δt. (c) Evaluate the limit of Δx/Δt as Δt approaches zero, to find the velocity at t = 3.00 s.
A particle moves along the x-axis according to the equation x = 2.00 + 3.00t - 1.00t², where x is in meters and t is in seconds. At t = 3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.
A particle moves along the x-axis according to the equation x = 2.00 + 3.00t - 1.00t², where x is in meters and t is in seconds. At t = 3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.
Flashcards
Non-zero velocity, zero acceleration?
Non-zero velocity, zero acceleration?
Yes, a particle can be moving at a constant speed (non-zero velocity) with zero acceleration.
Zero velocity, nonzero acceleration?
Zero velocity, nonzero acceleration?
Yes, a particle at rest (zero velocity) can experience acceleration, such as gravity causing an object to fall.
Velocity of car A > car B, acceleration comparison?
Velocity of car A > car B, acceleration comparison?
No, the faster velocity of car A does not dictate a greater acceleration than car B. Different accelerations are possible.
Average speed vs. average velocity
Average speed vs. average velocity
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Average speed calculation
Average speed calculation
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Average velocity calculation
Average velocity calculation
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Instantaneous speed at finish line
Instantaneous speed at finish line
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Constant vs non-uniform acceleration
Constant vs non-uniform acceleration
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Study Notes
Answers to Problem Sets
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Problem 7: If a particle's velocity is non-zero, its acceleration can be zero. A constant velocity means unchanging velocity, thus zero acceleration.
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Problem 8: If a particle's velocity is zero, its acceleration can be non-zero. An object dropped from rest accelerates due to gravity.
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Problem 9: A car exceeding another car's velocity doesn't necessarily mean it has a larger acceleration. Cars can have the same or different accelerations, or the second car may have recently accelerated more.
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Problem 13 (a): Secretariat's average speeds for each quarter mile segment are: first - 35.6 mi/h, second - 37.4 mi/h, third - 37.7 mi/h, final - 39.0 mi/h.
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Problem 13 (b): Secretariat's average acceleration during the race was 0.598 ft/s².
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Problem 18: Motion diagrams for various scenarios of constant and non-uniform acceleration. (diagrams described, but not included in the summary)
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Problem 3: Average velocities for given time intervals.
- 0 to 2s: 5 m/s
- 0 to 4 s: 1.2 m/s
- 2 to 4 s: -2.5 m/s
- 4 to 7 s: -3.3 m/s
- 0 to 8 s: 0 m/s
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Problem 5 (a): Average speed during the entire trip was 3.75 m/s.
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Problem 5 (b): Average velocity over the entire trip is 0 m/s because the walker starts and finishes at the same place.
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Problem 6:
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Position at 3 seconds was 27 meters.
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Position at 3.00s+𝞰t was 27.0m +(18.0m/s)𝞰t+(3.00m/s²)𝞰t²
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Velocity at 3.00 seconds was 18 m/s.
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Problem 15 (a): The particle's position at t = 3.00 seconds is 2.00 meters.
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Problem 15 (b): The particle's velocity at t = 3.00 seconds is -3.00 m/s.
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Problem 15 (c): The particle's acceleration is -2.00 m/s².
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