From the below information
Speed(m/sec) 2m at 0 sec, 4m at 2 sec, 6m at 3 sec, 8m at 4 sec, 10m at 5 sec.
Calculate acceleration.
Distance (I am getting answer as 27m but as per book it is 30m. Here as per table velocity is not uniform.) Plz confirm me the correct answer.
Thank you.
acceleration= changevelocty/time= (10m/s-2m/s)/5sec=8/5 m/s^2
distance= initialvel*time+1/2 acceleration*time^2
= 2*5+ 1/2*8/5*25=10+20=30m
Thank you Bob.
Can you please explain while I tried finding distance through area of triangles I did not get the same answer. With the given table I got two triangles shapes. One is 2 to 4 with 2 sec and other one is from 4 to 10 with time from 2sec to 5 sec. Rest of the shape I got is rectangles 0 to 4 with time 2 sec to 5 sec and 0 to 2 with time 0 to 2 sec.
Plz share your precious time. Thank you.
Hi Bob can u plz reply
To calculate acceleration, you need to determine the change in velocity over the change in time. In this case, you have the velocity at different time intervals.
From the given information:
- At 0 seconds, the velocity is 2 m/s.
- At 2 seconds, the velocity is 4 m/s.
- At 3 seconds, the velocity is 6 m/s.
- At 4 seconds, the velocity is 8 m/s.
- At 5 seconds, the velocity is 10 m/s.
To find the acceleration, you need to find the change in velocity between each interval. In this case, we can consider the intervals starting from 0 seconds and ending at each subsequent second.
The change in velocity can be calculated by subtracting the initial velocity from the final velocity. For example, the change in velocity during the first interval (from 0 sec to 2 sec) is 4 m/s - 2 m/s = 2 m/s.
Using this approach, let's calculate the changes in velocity for each interval:
- Interval 0 sec to 2 sec: 4 m/s - 2 m/s = 2 m/s
- Interval 2 sec to 3 sec: 6 m/s - 4 m/s = 2 m/s
- Interval 3 sec to 4 sec: 8 m/s - 6 m/s = 2 m/s
- Interval 4 sec to 5 sec: 10 m/s - 8 m/s = 2 m/s
Now, to find the acceleration, we need to determine the average change in velocity over the change in time. In this case, the change in time is 2 seconds for the first interval and 1 second for the subsequent intervals.
The average acceleration for each interval can be calculated by dividing the change in velocity by the change in time:
- Interval 0 sec to 2 sec: 2 m/s / 2 sec = 1 m/s^2
- Interval 2 sec to 3 sec: 2 m/s / 1 sec = 2 m/s^2
- Interval 3 sec to 4 sec: 2 m/s / 1 sec = 2 m/s^2
- Interval 4 sec to 5 sec: 2 m/s / 1 sec = 2 m/s^2
We now have the average accelerations for each interval. To find the overall acceleration, we can take the average of these values:
Average acceleration = (1 m/s^2 + 2 m/s^2 + 2 m/s^2 + 2 m/s^2) / 4 = 1.75 m/s^2
Therefore, the acceleration based on the given information is 1.75 m/s^2.
Now, let's calculate the distance traveled using the given information. Distance can be calculated by integrating the velocity with respect to time. However, since the velocity values are not continuous, we can approximate the distance traveled by considering each interval as a trapezoid and summing up the areas.
The distance traveled within each interval can be calculated by multiplying the average velocity of that interval by the time duration:
- Interval 0 sec to 2 sec: (2 m/s + 4 m/s) / 2 * 2 sec = 6 m
- Interval 2 sec to 3 sec: (4 m/s + 6 m/s) / 2 * 1 sec = 5 m
- Interval 3 sec to 4 sec: (6 m/s + 8 m/s) / 2 * 1 sec = 7 m
- Interval 4 sec to 5 sec: (8 m/s + 10 m/s) / 2 * 1 sec = 9 m
Now, let's sum up the distances traveled within each interval:
Total distance = 6 m + 5 m + 7 m + 9 m = 27 m
Therefore, based on the given information, the correct distance traveled is indeed 27 m.
If the book states that the correct distance is 30 m, there might be some additional information or assumptions stated that are not included in the table you provided. I would recommend referring to the book or the provided context to understand the discrepancy.