What graph BEST represents the relationship between velocity and time for an object that accelerates uniformly for 2 seconds, then moves at a constant velocity for 1 second, and finally decelerates for 3 seconds?
The best graph that represents the relationship between velocity and time for the given scenario would be a graph with three different sections:
1. The first section would be a straight line with a positive slope, representing the object's acceleration for 2 seconds.
2. The second section would be a straight line with a zero slope, representing the object's constant velocity for 1 second.
3. The third section would be a straight line with a negative slope, representing the object's deceleration for 3 seconds.
In summary, the graph would show an increasing velocity for 2 seconds, followed by a flat line representing constant velocity, and then a decreasing velocity for 3 seconds.
To determine the graph that best represents the relationship between velocity and time for the given scenario, we need to break down the different phases of the object's motion.
1. Acceleration phase (2 seconds): During this phase, the object accelerates uniformly. The velocity increases with time.
2. Constant velocity phase (1 second): The object moves at a constant velocity, which means the velocity remains the same for this period.
3. Deceleration phase (3 seconds): Here, the object decelerates, meaning its velocity decreases with time.
Now, let's consider each phase and their corresponding graphs:
1. Acceleration phase: The relationship between velocity and time during uniform acceleration is represented by a linear graph with a positive slope. This is because the velocity is increasing at a constant rate. The graph will be a straight line sloping upwards.
2. Constant velocity phase: During this phase, the object maintains a constant velocity, so the graph will be a horizontal line with no change in velocity over time.
3. Deceleration phase: In this phase, the object is slowing down, and the velocity decreases with time. The graph will be a line with a negative slope, representing the decreasing velocity.
Combining these phases, the best graph would consist of a straight line with a positive slope during the acceleration phase, followed by a horizontal line during the constant velocity phase, and then a straight line with a negative slope during the deceleration phase.
Therefore, the best graph that represents the relationship between velocity and time for the given scenario would have a positive slope for the first 2 seconds, followed by a horizontal line for the next 1 second, and finally a negative slope for the last 3 seconds.
The graph that best represents the relationship between velocity and time for the given scenario is a piecewise graph.
1. For the first 2 seconds, the object accelerates uniformly. This means that the velocity increases at a constant rate. The graph during this time will be a straight line with a positive slope.
2. After accelerating for 2 seconds, the object moves at a constant velocity for 1 second. This means that the velocity remains constant during this time. The graph during this time will be a horizontal line.
3. Finally, the object decelerates for 3 seconds. This means that the velocity decreases at a constant rate. The graph during this time will be a straight line with a negative slope.
Therefore, the graph representing the relationship between velocity and time for the scenario would consist of a positive sloping line followed by a horizontal line, and then a negative sloping line.