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 100 s per increment, and the scale for the velocity axis is 330 m/s per increment.
Well, let's have a look at this snowmobile's adventurous journey! In segment A, the velocity is constant at 0 m/s, which means that there is no change in velocity over time. So, the average acceleration during segment A would be a whopping 0 m/s². It's like the snowmobile decided to take a break and have a cup of hot cocoa!
Now, moving on to segment B. Here, the velocity is increasing at a steady rate from 0 m/s to 330 m/s over a time of 300 seconds. So, to calculate the average acceleration, we divide the change in velocity (330 m/s - 0 m/s) by the time interval (300 s). This gives us an average acceleration of 1.1 m/s². It's like the snowmobile just realized it's late for a snowball fight and suddenly zoomed off!
Finally, we arrive at segment C. In this segment, the velocity remains constant at 330 m/s, indicating no change in velocity over time. Hence, the average acceleration during segment C is once again 0 m/s². It's as if the snowmobile reached its top speed and decided to cruise along, enjoying the snowy scenery!
Now that we've analyzed each segment, it's safe to say that the snowmobile had a range of average accelerations: 0 m/s² in segments A and C, and a thrilling 1.1 m/s² in segment B. Hang on tight, my friend, it's going to be a bumpy, yet amusing, ride!
To determine the snowmobile's average acceleration during each segment, we need to calculate the slopes of the velocity-time graph for each segment. The slope of a velocity-time graph represents the acceleration.
Segment A:
To find the slope of segment A, we can choose any two points on the segment and calculate the change in velocity divided by the change in time.
Let's choose the points (200 s, 165 m/s) and (400 s, 0 m/s).
Change in velocity = final velocity - initial velocity
= 0 m/s - 165 m/s = -165 m/s
Change in time = final time - initial time
= 400 s - 200 s = 200 s
Average acceleration (segment A) = Change in velocity / Change in time
= -165 m/s / 200 s
≈ -0.825 m/s²
Segment B:
To find the slope of segment B, we can again choose any two points on the segment and calculate the change in velocity divided by the change in time.
Let's choose the points (600 s, 165 m/s) and (800 s, 330 m/s).
Change in velocity = final velocity - initial velocity
= 330 m/s - 165 m/s = 165 m/s
Change in time = final time - initial time
= 800 s - 600 s = 200 s
Average acceleration (segment B) = Change in velocity / Change in time
= 165 m/s / 200 s
= 0.825 m/s² (approximately)
Segment C:
To find the slope of segment C, we can again choose any two points on the segment and calculate the change in velocity divided by the change in time.
Let's choose the points (900 s, 330 m/s) and (1100 s, 0 m/s).
Change in velocity = final velocity - initial velocity
= 0 m/s - 330 m/s = -330 m/s
Change in time = final time - initial time
= 1100 s - 900 s = 200 s
Average acceleration (segment C) = Change in velocity / Change in time
= -330 m/s / 200 s
≈ -1.65 m/s²
Therefore, the snowmobile's average acceleration during segment A is approximately -0.825 m/s², during segment B is approximately 0.825 m/s², and during segment C is approximately -1.65 m/s².
To find the average acceleration during each segment, we need to calculate the change in velocity (Δv) divided by the change in time (Δt).
In segment A, the snowmobile's velocity changes from 0 m/s to 330 m/s over a time interval of 100 s. To find the change in velocity, we subtract the initial velocity from the final velocity: Δv = 330 m/s - 0 m/s = 330 m/s. The change in time is 100 s. Therefore, the average acceleration during segment A is Δv/Δt = 330 m/s / 100 s = 3.3 m/s².
In segment B, the snowmobile's velocity remains constant at 330 m/s. Since there is no change in velocity, the average acceleration is zero: Δv/Δt = 0 m/s / Δt = 0 m/s².
In segment C, the snowmobile's velocity changes from 330 m/s to 0 m/s over a time interval of 200 s. Using the same formula, the change in velocity is Δv = 0 m/s - 330 m/s = -330 m/s (negative sign indicates a decrease in velocity). The change in time is 200 s. Therefore, the average acceleration during segment C is Δv/Δt = -330 m/s / 200 s = -1.65 m/s².
So, the snowmobile's average acceleration during segment A is 3.3 m/s², during segment B is 0 m/s², and during segment C is -1.65 m/s².