To construct the velocity-time graph for the car's motion based on the provided information, let's break down the motion into three phases:
-
Acceleration Phase (0 to 15 seconds):
- The car starts from rest and accelerates uniformly to a speed of 30 m/s over 15 seconds.
- The velocity at the end of this phase is 30 m/s.
-
Constant Velocity Phase (15 to 45 seconds):
- The car maintains a constant speed of 30 m/s for 30 seconds.
- Velocity remains at 30 m/s during this entire interval.
-
Deceleration Phase (45 to 50 seconds):
- The car decelerates uniformly from 30 m/s to 0 m/s over a period of 5 seconds.
- The velocity at the end of this phase is 0 m/s.
Simplified Phases:
-
Acceleration (0 to 15s):
- From 0 m/s to 30 m/s in 15 seconds.
- This creates a straight line with a positive slope.
-
Constant Speed (15 to 45s):
- From 30 m/s to 30 m/s (horizontal line) from t = 15s to t = 45s.
-
Deceleration (45 to 50s):
- From 30 m/s to 0 m/s in 5 seconds.
- This creates a straight line with a negative slope.
Constructing the Velocity-Time Graph:
- X-axis will represent time (in seconds).
- Y-axis will represent velocity (in m/s).
- Start from the origin (0,0).
- Draw a line from (0,0) to (15,30) for acceleration.
- Draw a horizontal line from (15,30) to (45,30) for constant speed.
- Draw a line from (45,30) to (50,0) for deceleration.
The resulting graph should look like this:
Velocity (m/s)
30 | _____________
| |
| |
| |
| _________ |
| / |
0 |__________/___________|___________________________
0 15 45 50
Time (s)
Summary of Phases:
- 0 to 15s: Linear acceleration from 0 to 30 m/s.
- 15 to 45s: Constant velocity at 30 m/s.
- 45 to 50s: Linear deceleration from 30 m/s to 0 m/s.
This graph accurately represents the motion sequence of the car as described in the original problem.
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