The figure(Figure 1) is the velocity-versus-time graph of a 500 g particle that starts at x=0m and moves along the x-axis. Draw graphs of the following by calculating and plotting numerical values at t = 0, 1, 2, 3, and 4 s. Then sketch lines or curves of the appropriate shape between the points. Make sure you include appropriate scales on both axes of each graph.

Question

The figure(Figure 1) is the velocity-versus-time graph of a 500 g particle that starts at x=0m and moves along the x-axis. Draw graphs of the following by calculating and plotting numerical values at t = 0, 1, 2, 3, and 4 s. Then sketch lines or curves of the appropriate shape between the points. Make sure you include appropriate scales on both axes of each graph.

Answer 1

ok. Now what?

Answer 2

To draw the graphs of the following quantities based on the velocity-versus-time graph provided in Figure 1, we need to calculate and plot the numerical values at specific time intervals.

1. Displacement versus time (x-t) graph:
- To obtain the displacement at each time interval, we have to integrate the area under the velocity curve.
- Initially, we know that the particle starts at x = 0 m.
- Starting from t = 0 s, we calculate the area under the velocity curve up to each time interval using the trapezoidal rule.
- The trapezoidal rule states that the area under a curve between two points (t1, v1) and (t2, v2) is given by the formula (t2 - t1) * ((v1 + v2) / 2).
- By applying this formula to each time interval, we can calculate the displacement values.
- Plot the calculated displacement values against time on a graph, ensuring appropriate scales on both axes.

2. Acceleration versus time (a-t) graph:
- To obtain the acceleration at each time interval, we can differentiate the velocity curve.
- We can calculate the average acceleration between two time intervals using the formula (v2 - v1) / (t2 - t1).
- Calculating the average acceleration at each interval, we can plot the values against corresponding time intervals on a graph, ensuring appropriate scales.

3. Kinetic energy versus time (KE-t) graph:
- The kinetic energy (KE) of an object is given by the formula KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
- We can calculate the kinetic energy of the particle by substituting the values of mass and velocity at each time interval.
- Plotting the calculated kinetic energy values against time on a graph, ensuring appropriate scales.

Remember to label the axes, provide units, and connect the points on each graph with lines or curves of the appropriate shape based on the values calculated at the given time intervals.