From t = 0 to t = 3.30 min, a man stands still, and from t = 3.30 min to t = 6.60 min, he walks briskly in a straight line at a constant speed of 1.76 m/s. What are (a) his average velocity vavg and (b) his average acceleration aavg in the time interval 1.00 min to 4.30 min? What are (c) vavg and (d) aavg in the time interval 2.00 min to 5.30 min?
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avgvelociyt=total distance/total time
avg acceleratio=changevelociyt/total time
To calculate the average velocity and average acceleration, we will need to use the formulas:
(a) Average velocity (vavg) = displacement / time
(b) Average acceleration (aavg) = change in velocity / time
Given information:
t = 0 to t = 3.30 min: standing still
t = 3.30 min to t = 6.60 min: walking briskly at a constant speed of 1.76 m/s
Now, let's break down each part of the question:
(a) To find the average velocity vavg in the time interval 1.00 min to 4.30 min, we need to find the displacement during that time.
The man stands still from t = 0 to t = 1.00 min, so during this interval, his displacement is zero since he doesn't move.
From t = 1.00 min to t = 4.30 min, the man is walking briskly at a constant speed of 1.76 m/s. Therefore, his displacement during this interval can be calculated using the formula:
Displacement = velocity * time
Displacement = 1.76 m/s * (4.30 min - 1.00 min) = 1.76 m/s * 3.30 min
Now that we have the displacement, we can find the average velocity:
Average velocity = Displacement / Time (where Time = 4.30 min - 1.00 min)
Substitute the values to get:
Average velocity = (1.76 m/s * 3.30 min) / (4.30 min - 1.00 min)
(b) Moving on to average acceleration aavg, we need to find the change in velocity during the time interval 1.00 min to 4.30 min.
Since the man is initially standing still, his velocity is zero.
From t = 1.00 min to t = 4.30 min, his velocity remains constant at 1.76 m/s. So, the change in velocity is:
Change in velocity = Final velocity - Initial velocity
= 1.76 m/s - 0 m/s
= 1.76 m/s
Now, we can find average acceleration:
Average acceleration = Change in velocity / Time (where Time = 4.30 min - 1.00 min)
Substitute the values to get:
Average acceleration = (1.76 m/s) / (4.30 min - 1.00 min)
(c) To find vavg in the time interval 2.00 min to 5.30 min, follow the same steps as (a) but use the respective time interval.
(d) Similarly, to find aavg in the time interval 2.00 min to 5.30 min, follow the same steps as (b) but use the respective time interval.
By plugging in the given values into the formulas, you can now calculate the average velocity and average acceleration for the given time intervals.