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 60 s per increment, and the scale for the velocity axis is 270 m/s per increment.
Well, I must say, this snowmobile's journey seems to have more action than a rollercoaster! Let's break down the average accelerations, shall we?
In segment A, the velocity remains constant, which means the snowmobile isn't accelerating. So, its average acceleration during segment A would be as exciting as watching paint dry - a nice and solid 0 m/s².
Now, in segment B, the velocity ramped up pretty quickly. We can see that the slope of the graph is pretty steep, indicating a significant change in velocity. Therefore, the snowmobile's average acceleration during segment B would be positive and quite the rush!
Lastly, in segment C, the line becomes less steep, suggesting a decrease in velocity. This means the snowmobile is slowing down. So, the average acceleration during segment C would be negative, like trying to reverse time - a rather peculiar experience indeed!
Remember, though, these are just average accelerations, and the snowmobile's actual acceleration may be changing throughout each segment. But hey, at least we've got some entertaining physics to ponder, right?
To determine the snowmobile's average acceleration during each segment, we need to calculate the change in velocity divided by the change in time for each segment.
Segment A:
- Time interval: 4 increments * 60 s/increment = 240 s
- Velocity change: 3 increments * 270 m/s/increment = 810 m/s
Average acceleration in segment A = Velocity change / Time interval
= 810 m/s / 240 s
= 3.375 m/s²
Segment B:
- Time interval: 8 increments * 60 s/increment = 480 s
- Velocity change: -3 increments * 270 m/s/increment = -810 m/s (negative because the velocity is decreasing)
Average acceleration in segment B = Velocity change / Time interval
= -810 m/s / 480 s
= -1.6875 m/s² (negative because the velocity is decreasing)
Segment C:
- Time interval: 10 increments * 60 s/increment = 600 s
- Velocity change: 3 increments * 270 m/s/increment = 810 m/s
Average acceleration in segment C = Velocity change / Time interval
= 810 m/s / 600 s
= 1.35 m/s²
Therefore, the snowmobile's average acceleration during segments A, B, and C are:
Segment A: 3.375 m/s²
Segment B: -1.6875 m/s²
Segment C: 1.35 m/s²
To find the average acceleration during each segment, we need to use the formula:
Average acceleration = Change in velocity / Change in time
Segment A:
To find the change in velocity and change in time for segment A, we need to determine the initial and final velocity and the time interval for this segment.
Looking at the velocity-time graph, we can see that the initial velocity is 0 m/s, and the final velocity is 270 m/s. The time interval for segment A is 60 seconds.
Change in velocity (Δv) = final velocity - initial velocity
= 270 m/s - 0 m/s
= 270 m/s
Change in time (Δt) = 60 seconds
Average acceleration for segment A = (Δv) / (Δt)
= 270 m/s / 60 s
= 4.5 m/s²
Segment B and C:
The process is the same for segments B and C. We need to find the change in velocity and the change in time for each segment.
Segment B:
The initial velocity is 270 m/s, and the final velocity is also 270 m/s. The time interval for segment B is 120 seconds.
Change in velocity (Δv) = final velocity - initial velocity
= 270 m/s - 270 m/s
= 0 m/s
Change in time (Δt) = 120 seconds
Average acceleration for segment B = (Δv) / (Δt)
= 0 m/s / 120 s
= 0 m/s²
Segment C:
The initial velocity is 270 m/s, and the final velocity is 0 m/s. The time interval for segment C is 240 seconds.
Change in velocity (Δv) = final velocity - initial velocity
= 0 m/s - 270 m/s
= -270 m/s (negative because the velocity decreases)
Change in time (Δt) = 240 seconds
Average acceleration for segment C = (Δv) / (Δt)
= -270 m/s / 240 s
= -1.125 m/s²
So, the average acceleration during segment A is 4.5 m/s², during segment B is 0 m/s², and during segment C is -1.125 m/s².
Segment A 540-0/120-0 =4.5
Segment B 0-0/0-0 = 0
Segment C 1080-540/288 = 7.5