To draw the velocity-time graph for the car's motion based on the provided information, we can break down the motion into three phases:
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Acceleration Phase:
- Duration: 15 seconds
- Initial Velocity: 0 m/s (starts from rest)
- Final Velocity: 30 m/s
Since the car accelerates uniformly from 0 m/s to 30 m/s in 15 seconds, the velocity increases linearly.
-
Constant Velocity Phase:
- Duration: 30 seconds
- Velocity: 30 m/s
During this phase, the velocity remains constant.
-
Deceleration Phase:
- Duration: 5 seconds
- Initial Velocity: 30 m/s
- Final Velocity: 0 m/s (comes to rest)
The car decelerates uniformly, which means the velocity decreases linearly back to 0 m/s.
Steps to Plot:
-
Acceleration Phase (0 to 15 seconds):
- A line starts at the origin (0,0) and reaches the point (15, 30) on the graph (15 seconds and 30 m/s).
-
Constant Velocity Phase (15 to 45 seconds):
- From (15, 30) to (45, 30), draw a horizontal line at 30 m/s for 30 seconds.
-
Deceleration Phase (45 to 50 seconds):
- From (45, 30) to (50, 0), draw a line that slopes downward from 30 m/s to 0 m/s over 5 seconds.
Resulting Graph Description:
- The graph consists of three segments:
- An increasing linear segment from (0, 0) to (15, 30).
- A horizontal line segment from (15, 30) to (45, 30).
- A decreasing linear segment from (45, 30) to (50, 0).
Overall Structure
- X-axis: Time in seconds (0 to 50 s)
- Y-axis: Velocity in m/s (from 0 to 30 m/s)
- The graph should have a slope for the first section, be flat in the second, and have a downward slope in the third section.
If you were to sketch this, you would end up with a triangular shape for the acceleration and deceleration phases and a rectangle for the constant velocity phase.
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