a particle is moving with a velocity of 6m/s when subjected to an accelaration of -3m/s for 4 seconds.it then moves with a constant velocity for 2 seconds.draw a velocity-time graph.
To draw the velocity-time graph, we need to understand how the velocity of the particle changes over time.
Let me break down the information provided step by step:
1. The initial velocity of the particle is given as 6 m/s.
2. The particle is subjected to an acceleration of -3 m/s for 4 seconds.
3. After that, the particle moves with a constant velocity for 2 seconds.
Now, let's analyze each phase and determine how the velocity changes:
Phase 1: Acceleration phase
- The particle has an initial velocity of 6 m/s.
- The acceleration is given as -3 m/s.
- The time duration for this phase is 4 seconds.
During this phase, the particle is slowing down due to the negative acceleration. To find the final velocity after 4 seconds, we can use the formula:
Final velocity = Initial velocity + (Acceleration × Time)
Final velocity = 6 m/s + (-3 m/s × 4 s)
Final velocity = 6 m/s - 12 m/s
Final velocity = -6 m/s
Phase 2: Constant velocity phase
- The particle moves with a constant velocity for 2 seconds.
- The velocity during this phase remains -6 m/s since there is no acceleration.
Now, we have the necessary information to plot the velocity-time graph:
- On the x-axis, plot the time in seconds.
- On the y-axis, plot the velocity in m/s.
Starting from the origin:
- Mark the initial velocity of the particle as 6 m/s at time t = 0.
- From there, draw a straight line with a negative slope to the point where t = 4 seconds and the velocity is -6 m/s.
- Continue the graph as a horizontal line at -6 m/s for the next 2 seconds.
The resulting graph should look like this:
^
| ___________
6 | | |
| | |
| | |
0 |________________|__________|______________>
0 4 6 8
Time (s)
Note: The graph represents the velocity of the particle against time, and the negative slope during the acceleration phase indicates deceleration or slowing down.