A car moves at 12 m/s for 30.0 seconds. It then accelerates at 1.5 m/s^2 for 8.00 seconds.
Finally, it continues on at this top speed for another 12.0 seconds. Calculate the net displacement during the whole time interval.
Doesn't elaborate or explain anything😵
To calculate the net displacement during the entire time interval, we need to break down the motion into different stages and calculate the displacement for each stage.
1. Stage 1: Initial constant velocity motion
- Velocity (v1) = 12 m/s
- Time (t1) = 30.0 s
- Displacement (s1) = v1 * t1 = 12 m/s * 30.0 s = 360 m
2. Stage 2: Acceleration
- Acceleration (a2) = 1.5 m/s^2
- Time (t2) = 8.00 s
Now we need to calculate the displacement during this stage. We can use the equation:
s2 = v2 * t2 + 0.5 * a2 * (t2)^2
To find the final velocity (v2), we can use the formula:
v2 = v1 + a2 * t2
v2 = 12 m/s + 1.5 m/s^2 * 8.00 s = 24 m/s
Substituting the values:
s2 = 24 m/s * 8.00 s + 0.5 * 1.5 m/s^2 * (8.00 s)^2
s2 = 192 m + 48 m = 240 m
3. Stage 3: Constant velocity motion
- Velocity (v3) = 24 m/s
- Time (t3) = 12.0 s
- Displacement (s3) = v3 * t3 = 24 m/s * 12.0 s = 288 m
Now, we can add the displacements of all three stages to find the net displacement:
Net displacement = s1 + s2 + s3 = 360 m + 240 m + 288 m = 888 m
Therefore, the net displacement during the whole time interval is 888 meters.
To calculate the net displacement during the whole time interval, we need to calculate the displacement during each segment of the motion and then add them together.
1. During the first segment, the car moves at a constant speed of 12 m/s for 30.0 seconds.
The displacement during this segment can be calculated using the formula: displacement = velocity × time.
So, the displacement during this segment is: 12 m/s × 30.0 s = 360 meters.
2. During the second segment, the car accelerates at 1.5 m/s^2 for 8.00 seconds.
The displacement during this segment can be calculated using the formula: displacement = initial velocity × time + 0.5 × acceleration × time^2.
Since the car starts from rest, the initial velocity is 0 m/s.
So, the displacement during this segment is: 0 × 8.00 s + 0.5 × 1.5 m/s^2 × (8.00 s)^2 = 48 meters.
3. During the third segment, the car continues at this top speed (12 m/s) for another 12.0 seconds.
The displacement during this segment can be calculated using the same formula as in the first segment: displacement = velocity × time.
So, the displacement during this segment is: 12 m/s × 12.0 s = 144 meters.
Now, we can calculate the net displacement by adding up the individual displacements:
Net displacement = displacement in first segment + displacement in second segment + displacement in third segment
= 360 meters + 48 meters + 144 meters
= 552 meters.
Therefore, the net displacement during the whole time interval is 552 meters.
1st part ... d = 12 m/s * 30.0 s
2nd part ... ave speed = {12 m/s + [12 m/s + (1.5 m/s^2 * 8.00 s)]} / 2
... d = ave speed * 8.00 s
3rd part ... top speed = 12 m/s + (1.5 m/s^2 * 8.00 s)
... d = top speed * 12.0 s
add the displacements for the total