To sketch the position vs time graph, we need to integrate the velocity vs time graph. We can break down the trip into three sections: the acceleration phase, the constant velocity phase, and the deceleration phase.
(a) Position vs time graph:
1. Acceleration phase (from 0 s to 3 s):
Since the elevator starts from rest and accelerates, the velocity vs time graph will be a straight line with a positive slope. Integrating this part will give us a parabolic curve for the position vs time graph.
2. Constant velocity phase (from 3 s to 18 s):
During this phase, the elevator maintains a constant velocity, which means the velocity vs time graph will be a horizontal line. Integrating a horizontal line will give us a straight line in the position vs time graph.
3. Deceleration phase (from 18 s to 23 s):
The elevator decelerates, so the velocity vs time graph will be a straight line with a negative slope. Integrating this part will give us a parabolic curve for the position vs time graph.
Overall, the position vs time graph will look like this:
```
| __________
| / \
| / \
| / \
| / \
______|/_________________\_____
0s 3s 18s 23s
```
(b) Acceleration vs time graph:
From the given information, we know the elevator accelerates for 3 seconds, maintains a constant velocity for 15 seconds, and then decelerates for 5 seconds.
The acceleration vs time graph will look like this:
```
/|
/ |
/ |
/ |
/____|\
0s 3s 18s 23s
```
The acceleration is initially positive during the acceleration phase, then becomes zero during the constant velocity phase, and finally becomes negative during the deceleration phase.
Consider the velocity vs time graph of a person in an elevator shown in. Suppose the elevator is initially at rest. It than accelerates from 3 seconds maintain that velocity for 15 seconds, than decelerate to 5 seconds from motion equation for constant acceleration in one dimension for the complete trip. (We could however, use them in three individual section where acceleration is constant.) Sketch graphs of (a) position vs time (b) acceleration vs time for the trip
1 answer