Using the velocity versus time graph, calculate the acceleration of Object A.
The points for Object A are: (1, 3), (2, 6), (3, 9), (4, 12).
The points for Object B are: (0, 10), (1, 8), (2, 6), (3, 9), (4, 2) *(sorry I cannot upload the graph)
A) 3 m/s2
3 m per s squared
B) −3 m/s2
negative 3 m per s squared
C) 0.33 m/s2
0.33 m per s squared
D) −0.33 m/s2
negative 0.33 m per s squared
A) 3 m/s2
Ah, the good ol' velocity versus time graph. Let's see what we've got here. Now, to calculate the acceleration of Object A, we need to look at the change in velocity over the change in time.
The points for Object A give us a nice straight line, showing a constant increase in velocity. So, let's take the first and last points, (1, 3) and (4, 12), respectively.
The change in velocity is given by (final velocity - initial velocity), which is (12 - 3) = 9 m/s.
The change in time is given by (final time - initial time), which is (4 - 1) = 3 s.
To calculate acceleration, we divide the change in velocity by the change in time. So, 9 m/s divided by 3 s gives us an acceleration of 3 m/s².
Therefore, the correct answer is A) 3 m/s². So, Object A is accelerating at a rate of 3 meters per second squared. Keep on zooming, Object A!
To calculate the acceleration of Object A using the velocity versus time graph, we need to calculate the slope of the graph. The slope represents the rate of change of velocity, which is the acceleration.
Using the points given for Object A: (1, 3), (2, 6), (3, 9), (4, 12), we can calculate the acceleration by finding the difference in velocities and dividing it by the difference in time.
First, let's calculate the difference in velocity for each time interval:
- The difference between (2, 6) and (1, 3) is 6 - 3 = 3 m/s.
- The difference between (3, 9) and (2, 6) is 9 - 6 = 3 m/s.
- The difference between (4, 12) and (3, 9) is 12 - 9 = 3 m/s.
Next, let's calculate the difference in time for each interval:
- The difference between 2 and 1 is 2 - 1 = 1 s.
- The difference between 3 and 2 is 3 - 2 = 1 s.
- The difference between 4 and 3 is 4 - 3 = 1 s.
Now, let's calculate the acceleration by dividing the difference in velocity by the difference in time for each interval:
- The acceleration for the interval between (1, 3) and (2, 6) is 3 m/s / 1 s = 3 m/s^2.
- The acceleration for the interval between (2, 6) and (3, 9) is 3 m/s / 1 s = 3 m/s^2.
- The acceleration for the interval between (3, 9) and (4, 12) is 3 m/s / 1 s = 3 m/s^2.
Since the acceleration is constant for all intervals and equal to 3 m/s^2, the answer is:
A) 3 m/s^2
To calculate the acceleration of Object A using the velocity versus time graph, we need to find the slope of the graph. The slope of a velocity versus time graph represents the acceleration.
First, we need to determine the change in velocity and the time interval for each segment of the graph.
Segment 1:
Initial velocity = 3 m/s
Final velocity = 6 m/s
Time interval = (2 - 1) s = 1s
Change in velocity = Final velocity - Initial velocity = 6 m/s - 3 m/s = 3 m/s
Acceleration = Change in velocity / Time interval = 3 m/s / 1s = 3 m/s^2
Segment 2:
Initial velocity = 6 m/s
Final velocity = 9 m/s
Time interval = (3 - 2) s = 1s
Change in velocity = Final velocity - Initial velocity = 9 m/s - 6 m/s = 3 m/s
Acceleration = Change in velocity / Time interval = 3 m/s / 1s = 3 m/s^2
Segment 3:
Initial velocity = 9 m/s
Final velocity = 12 m/s
Time interval = (4 - 3) s = 1s
Change in velocity = Final velocity - Initial velocity = 12 m/s - 9 m/s = 3 m/s
Acceleration = Change in velocity / Time interval = 3 m/s / 1s = 3 m/s^2
Since the acceleration remains constant at 3 m/s^2 throughout all the segments, the answer is option A) 3 m/s^2.