Question

Plot the velocity on the velocity-time graph and then, find the displacement

Answer 1

To find displacement from a velocity-time graph, you calculate the area under the graph's line. The slope of the velocity-time graph indicates acceleration, and the area under a constant velocity line directly gives you the displacement.

Step-by-step explanation:

To plot velocity on a velocity-time graph and to find the displacement, you follow a procedure where you first graph the velocity against time and then use this graph to calculate the displacement. The key concept here is that the area under the velocity vs. time graph represents the displacement.

Understanding Velocity-Time Graphs

The procedure starts by plotting velocity on the y-axis against time on the x-axis. If the graph shows a constant velocity, the line will be horizontal. In scenarios where the object's velocity is changing, the slope of that line will represent the acceleration.

Calculating Displacement

To find the displacement from a velocity-time graph, you calculate the area under the graph's line. This area corresponds to the total distance traveled in the direction of motion. If you're working with a graph that is a straight line, these calculations are usually simpler.

For instance, if a graph shows a constant velocity of 0.5 km/minute for 10 minutes, finding the displacement would involve multiplying these two values. The resulting displacement would be 5 km. If your graph includes sections where the velocity is negative (implying a change in direction), those areas would be subtracted from the overall displacement.

Answer 2

ANSWER and EXPLANATION

To plot the velocity at different times, we have to find the slope of the graph at those times.

So, we find the slope between 0 - 1, 0 - 2, 0 - 3, and 0 - 4 seconds using the formula:

`v=\frac{p_2-p_1_{}_{}}{t_2-t_1}`

Therefore, we have that the velocity at the time intervals is as follows:

`\begin{gathered} \Rightarrow v(0,1)=(1-0)/(1-0)=(1)/(1)=1\text{ m/s} \\ \Rightarrow v(0,2)=(2-0)/(2-0)=(2)/(2)=1\text{ m/s} \\ \Rightarrow v(0,3)=(3-0)/(3-0)=(3)/(3)=1\text{ m/s} \\ \Rightarrow v(0,4)=(4-0)/(4-0)=(4)/(4)=1\text{ m/s} \end{gathered}`

As we can see, the velocity is constant throughout the motion.

Now, we have to plot this information on the velocity-time graph

To find the displacement from the graph, we have to find the area of the rectangle that has the vertices (0, 0), (4, 0), (4, 1), and (0, 1).

The area of a rectangle is given as:

`A=L\cdot W`

where L = length, W = width

The length of the rectangle is the horizontal distance between (4, 0) and (0, 0) which is 4 and the width is the vertical distance between (0, 1) and (0, 0) which is 1.

Therefore, the displacement (area under the graph) is:

`\begin{gathered} A=4\cdot1 \\ A=4m \end{gathered}`