A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during each of the segments A, B, and C? The scale for the time axis is 30 s per increment, and the scale for the velocity axis is 50 m/s per increment.
Well, I must say, this snowmobile is quite the graph superstar! Now, let's analyze each segment, shall we?
Segment A: Ah, the good ol' positive slope. This means the velocity is increasing over time. So, the average acceleration during Segment A is simply positive. It's like the snowmobile is saying, "I'm going faster and faster, folks!"
Segment B: Ah, the flat line. This means that the velocity is constant, which implies zero acceleration. The snowmobile is probably taking a break, enjoying the ride while maintaining a steady speed. Can't blame them, it's a lovely sight out there!
Segment C: Now, this one is a bit tricky. We have a negative slope, indicating that the velocity is decreasing over time. So, the average acceleration during Segment C is negative. The snowmobile is thinking, "Time to slow down and take it easy!"
Remember, acceleration is all about the change in velocity over time. So, in Segment A, it's positive because velocity is increasing; in Segment B, it's zero because velocity is constant; and in Segment C, it's negative because velocity is decreasing.
To determine the average acceleration for each segment, we need to calculate the change in velocity and divide it by the change in time for each segment.
Segment A:
From the graph, the change in velocity can be calculated as the difference in the y-values at the start and end points of segment A. The initial velocity is 0 m/s, and the final velocity is 100 m/s. Therefore, the change in velocity for segment A is 100 m/s - 0 m/s = 100 m/s.
The time interval for segment A is given by the difference in the x-values at the start and end points of segment A. The time at the start point is 0 s, and the time at the end point is 60 s. Therefore, the change in time for segment A is 60 s - 0 s = 60 s.
Using the formula for average acceleration:
Average acceleration (A) = Change in velocity / Change in time
Average acceleration (A) = 100 m/s / 60 s ≈ 1.67 m/s²
Segment B:
From the graph, the change in velocity for segment B is 0 m/s, so the acceleration during this segment is 0 m/s².
Segment C:
From the graph, the change in velocity can be calculated as the difference in the y-values at the start and end points of segment C. The initial velocity is 100 m/s, and the final velocity is -100 m/s. Therefore, the change in velocity for segment C is -100 m/s - 100 m/s = -200 m/s.
The time interval for segment C is given by the difference in the x-values at the start and end points of segment C. The time at the start point is 90 s, and the time at the end point is 150 s. Therefore, the change in time for segment C is 150 s - 90 s = 60 s.
Average acceleration (C) = Change in velocity / Change in time
Average acceleration (C) = -200 m/s / 60 s ≈ -3.33 m/s²
In summary, the average accelerations for each segment are as follows:
Segment A: 1.67 m/s²
Segment B: 0 m/s²
Segment C: -3.33 m/s²
To determine the average acceleration during each segment, we need to calculate the change in velocity and divide it by the change in time for each segment.
Segment A:
To find the change in velocity for segment A, we need to determine the difference between the initial velocity and the final velocity. Looking at the graph, at the beginning of segment A, the initial velocity is 0 m/s, and at the end of segment A, the final velocity is 50 m/s.
Change in velocity = Final velocity - Initial velocity = 50 m/s - 0 m/s = 50 m/s
The time increment for each increment on the graph is 30 s. Segment A covers 2 increments, so the change in time is:
Change in time = Number of increments * Time increment = 2 * 30 s = 60 s
Average acceleration for segment A:
Acceleration = Change in velocity / Change in time = 50 m/s / 60 s = 0.83 m/s²
Segment B:
For segment B, the initial velocity is 50 m/s, and the final velocity is 100 m/s.
Change in velocity = Final velocity - Initial velocity = 100 m/s - 50 m/s = 50 m/s
Segment B covers 4 increments, so the change in time is:
Change in time = Number of increments * Time increment = 4 * 30 s = 120 s
Average acceleration for segment B:
Acceleration = Change in velocity / Change in time = 50 m/s / 120 s ≈ 0.42 m/s²
Segment C:
In segment C, the initial velocity is 100 m/s, and the final velocity is 0 m/s.
Change in velocity = Final velocity - Initial velocity = 0 m/s - 100 m/s = -100 m/s
Segment C covers 3 increments, so the change in time is:
Change in time = Number of increments * Time increment = 3 * 30 s = 90 s
Average acceleration for segment C:
Acceleration = Change in velocity / Change in time = -100 m/s / 90 s ≈ -1.11 m/s²
Therefore, the snowmobile's average acceleration during segment A is 0.83 m/s², during segment B is 0.42 m/s², and during segment C is -1.11 m/s².