A ball rolling down an incline travels 6.0 cm in the first 0.25 econds, and 24 cm in the first 0.50 seconds. Find:
a)The average speed for the first quarter second time interval
B) The average speed for the second time interval
C) Find its acceleration
a) 6/.25 = 24 cm/s = .24 m/s
b) 24/.5 = 48 cm/s = .48 m/s
c) need exact speed at center of intervals, it is half that at the end of the interval since the intervals start with velocity zero and v linear with time
speed at .125 seconds = 24 cm/s = .24 m/s
speed at .25 seconds = 48 = .48 m/s
change in speed /change in time = (48-24)/(.25-.125)
= 24/(1/8) = 24*8 = 192 cm/s^2 = 1.92 m/s^2
a) The average speed for the first quarter-second time interval can be found by dividing the distance traveled (6.0 cm) by the time taken (0.25 seconds):
Average speed = distance / time
Average speed = 6.0 cm / 0.25 seconds
Average speed = 24 cm/s
b) The average speed for the second time interval can be found by dividing the distance traveled (24 cm) by the time taken (0.50 seconds):
Average speed = distance / time
Average speed = 24 cm / 0.50 seconds
Average speed = 48 cm/s
c) To find the acceleration, we can use the equation:
Acceleration = (final velocity - initial velocity) / time
For the first time interval, the initial velocity is 0 cm/s and the final velocity can be found by dividing the distance traveled (6.0 cm) by the time taken (0.25 seconds):
Final velocity = distance / time
Final velocity = 6.0 cm / 0.25 seconds
Final velocity = 24 cm/s
Plugging in these values:
Acceleration = (24 cm/s - 0 cm/s) / 0.25 seconds
Acceleration = 96 cm/s^2
For the second time interval, the initial velocity is 24 cm/s (from the first interval) and the final velocity can be found by dividing the distance traveled (24 cm) by the time taken (0.50 seconds):
Final velocity = distance / time
Final velocity = 24 cm / 0.50 seconds
Final velocity = 48 cm/s
Plugging in these values:
Acceleration = (48 cm/s - 24 cm/s) / 0.50 seconds
Acceleration = 48 cm/s - 24 cm/s / 0.50 seconds
Acceleration = 24 cm/s / 0.50 seconds
Acceleration = 48 cm/s^2
So, the acceleration is 96 cm/s^2 for the first time interval and 48 cm/s^2 for the second time interval.
To find the average speed for each time interval and the acceleration of the ball rolling down the incline, we can use the formulas:
Average Speed = Distance / Time
Acceleration = Change in Velocity / Time
a) The average speed for the first quarter-second time interval:
Distance = 6.0 cm
Time = 0.25 seconds
Average Speed = 6.0 cm / 0.25 seconds
To find the average speed, divide the distance traveled by the time taken.
b) The average speed for the second time interval:
Distance = 24 cm
Time = 0.50 seconds
Average Speed = 24 cm / 0.50 seconds
Again, divide the distance traveled by the time taken to find the average speed.
c) To find the acceleration, we need to find the change in velocity. However, we only have the distance covered and the time taken.
We can use the equation of motion:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time^2)
In the first quarter-second time interval, the distance covered is 6.0 cm, and the time taken is 0.25 seconds.
6.0 cm = (Initial Velocity × 0.25 s) + (0.5 × Acceleration × 0.25 s^2)
In the second time interval, the distance covered is 24 cm, and the time taken is 0.50 seconds.
24 cm = (Initial Velocity × 0.50 s) + (0.5 × Acceleration × 0.50 s^2)
We have two equations and two unknowns (Initial Velocity and Acceleration). By solving these equations simultaneously, we can find the values of Initial Velocity and Acceleration.
Note: If the initial velocity is known or assumed to be zero, we can simplify the equations and find the acceleration directly by substituting the given values.
A ball rolling down an incline travels 6.0 cm in the first 0.25 seconds, and 24 cm in the first 0.50 seconds. What is the average speed for the first quarter second time interval? average speed for the second quarter second time interval? its acceleration?
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