A car starts from rest and accelerate uniformly until it reaches a speed of 30m/s after 15s. It then maintains this speed for another 30s then the car decelerates uniformly until it is brought to rest after a further 5 seconds.

Question

Draw the velocity time graph of the motion of the car

Answer 1

To draw the velocity-time graph for the motion of the car based on the given information, we can break down the movements into three distinct phases:

1. Acceleration Phase (0 to 15 seconds):

   • The car starts from rest (0 m/s) and accelerates to 30 m/s in 15 seconds.
   • Since the acceleration is uniform, the velocity increases linearly.
   • The slope of this segment is \( \frac{30 \text{ m/s} - 0 \text{ m/s}}{15 \text{ s} - 0 \text{ s}} = 2 \text{ m/s}^2 \).

2. Constant Speed Phase (15 to 45 seconds):

   • The car maintains a constant speed of 30 m/s for 30 seconds.
   • This segment is represented as a horizontal line at 30 m/s on the graph from 15 seconds to 45 seconds.

3. Deceleration Phase (45 to 50 seconds):

   • The car decelerates uniformly from 30 m/s to 0 m/s over 5 seconds.
   • The slope of this segment is \( \frac{0 \text{ m/s} - 30 \text{ m/s}}{50 \text{ s} - 45 \text{ s}} = -6 \text{ m/s}^2 \).
   • This represents a straight line sloping downwards from 30 m/s to 0 m/s over the last 5 seconds.

Velocity-Time Graph

The resulting graph can be visualized as follows:

1. From (0, 0) to (15, 30): A straight line with a positive slope (indicating acceleration).
2. From (15, 30) to (45, 30): A horizontal line at 30 m/s (indicating constant speed).
3. From (45, 30) to (50, 0): A straight line with a negative slope (indicating deceleration).

Points of Interest:

• At 0 seconds, the velocity is 0 m/s.
• At 15 seconds, the velocity reaches 30 m/s.
• From 15 to 45 seconds, the velocity remains at 30 m/s.
• At 45 seconds, the velocity is still 30 m/s.
• At 50 seconds, the velocity returns to 0 m/s.

Sketch:

Here's how the graph can be visualized:

Velocity (m/s)
|
|              *
|              |
|              |
|              |                ___________
|              |               |
|              |               |
|              |               |
|              |               |
|     *       |               |
|      \      |               |
|       \     |               |
|        *    |               |
|         |   |               |
|         |   |               |
|         |   |               |
|         |   *               |
|---------|---|---|---|---|---|---|---|---|---|---|--- Time (s)
          0   5  10  15  20  25  30  35  40  45  50

• The "*" indicates points where the velocity is measured at each significant phase mentioned.
• The lines illustrate the nature of the acceleration, constant speed, and deceleration.

You can use graphing tools to better illustrate this diagram based on the points and phases described.