To draw the velocity-time graph, we first need to break down the movement into two parts: the acceleration phase and the constant velocity phase.
1. Acceleration Phase (0-4 seconds):
During this phase, the component is uniformly accelerated from 3 m/s to 8 m/s. The initial velocity is 3 m/s, and the final velocity is 8 m/s. The time taken is 4 seconds.
To find the acceleration, we use the formula:
acceleration = (final velocity - initial velocity) / time taken
acceleration = (8 m/s - 3 m/s) / 4s = 1 m/s²
To draw this phase on the velocity-time graph, we start at the initial velocity of 3 m/s and draw a straight line with a gradient of 1 m/s² for 4 seconds until we reach the final velocity of 8 m/s.
2. Constant Velocity Phase (4-6 seconds):
During this phase, the component moves in a straight track at a constant velocity of 8 m/s. The time taken is 2 seconds.
To draw this phase on the velocity-time graph, we draw a horizontal line at the velocity of 8 m/s for 2 seconds.
Putting both phases together, the velocity-time graph would look like this:
| ........
|. : :
Velocity |....:. :
(m/s) | : :
| : :
|____:______:_____________
4s 6s
To determine the displacement of the component for a time of 6 seconds, we need to find the area under the velocity-time graph from 0 to 6 seconds.
1. Area of the acceleration phase rectangle:
The base of the rectangle is 4 seconds and the height is the change in velocity, which is (8 m/s - 3 m/s) = 5 m/s.
Area of the rectangle = base * height = 4s * 5 m/s = 20 m
2. Area of the constant velocity phase rectangle:
The base of the rectangle is 2 seconds and the height is the constant velocity, which is 8 m/s.
Area of the rectangle = base * height = 2s * 8 m/s = 16 m
Total displacement = area of acceleration phase rectangle + area of constant velocity phase rectangle
Total displacement = 20 m + 16 m = 36 m
Therefore, the displacement of the component for a time of 6 seconds is 36 meters.
A component is uniformly accelerated in a production plant from 3 m/s to 8 m/s in 4 s, and then moves in a straight track at a constant velocity of 8 m/s for the following 2 s. Draw a suitable velocity-time graph for this movement and determine from the graph the displacement of the component for a time of 6 s.
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