From t = 0 to t = 3.72 min, a man stands still, and from t = 3.72 min to t = 7.44 min, he walks briskly in a straight line at a constant speed of 2.53 m/s. What are (a) his average velocity avg and (b) his average acceleration avg in the time interval 1.00 min to 4.72 min? What are (c) avg and (d) avg in the time interval 2.00 min to 5.72 min?
distance = speed * time
(a) avg speed = total_distance/total_time = (7.44-3.72)s*2.53m/s / (7.44-0)s = 1.265 m/s
(b) avg acceleration = change_in_speed/time
now just plug and chug
To calculate average velocity and average acceleration, we need to first determine the displacement and change in velocity values during each time interval.
(a) Average velocity in the time interval 1.00 min to 4.72 min:
To find the average velocity, we need to calculate the total displacement and divide it by the total time.
Displacement = Final position - Initial position
At t = 1.00 min, the man is standing still, so his position hasn't changed from the initial position.
At t = 4.72 min, he has already started walking briskly, with a constant speed of 2.53 m/s.
Let's calculate the total displacement:
Displacement = Final position - Initial position
= (2.53 m/s) * (4.72 min - 1.00 min)
Note: Be sure to use consistent units for the calculations. Here, we converted minutes to seconds.
(b) Average acceleration in the time interval 1.00 min to 4.72 min:
To find the average acceleration, we need to calculate the change in velocity and divide it by the time interval.
Change in Velocity = Final Velocity - Initial Velocity
At t = 1.00 min, the man is standing still, so his initial velocity is 0 m/s.
At t = 4.72 min, he is already walking briskly at a constant velocity of 2.53 m/s.
Now let's calculate the change in velocity:
Change in Velocity = Final Velocity - Initial Velocity
= 2.53 m/s - 0 m/s
To find the average acceleration, divide the change in velocity by the time interval.
(c) Average velocity in the time interval 2.00 min to 5.72 min:
To find the average velocity, we need to calculate the total displacement and divide it by the total time.
Recall that at t = 2.00 min, the man has already started walking briskly.
Let's calculate the total displacement:
Displacement = Final position - Initial position
= (2.53 m/s) * (5.72 min - 2.00 min)
(d) Average acceleration in the time interval 2.00 min to 5.72 min:
To find the average acceleration, we need to calculate the change in velocity and divide it by the time interval.
Recall that at t = 2.00 min, the man has already started walking briskly.
Calculate the change in velocity:
Change in Velocity = Final Velocity - Initial Velocity
= 2.53 m/s - 2.53 m/s
To find the average acceleration, divide the change in velocity by the time interval.