The position versus time for a certain object
moving along the x-axis is shown. The object’s initial position is −3 m. Find the instantaneous velocity at 8 s.
Answer in units of m/s.
no diagrams work here.
But the desired velocity is the slope of the graph at x=8
If the graph is piecewise linear, that should be easy to determine.
To find the instantaneous velocity at a specific time, we need to calculate the derivative of the position-time function. In this case, we have the position-time graph provided.
To get the instantaneous velocity at a given time, we can find the slope of the tangent line to the position-time graph at that specific time. The slope of the tangent line represents the object's velocity at that moment.
Now let's find the slope at 8 seconds. Look at the tangent line near t = 8 seconds and choose two points that lie on the line. For example, we can choose two points approximately at t = 7.8 seconds and t = 8.2 seconds.
Measure the vertical change (change in position) and the horizontal change (change in time) between these two points. Then calculate the slope of the tangent line by dividing the change in position by the change in time. This will give us the instantaneous velocity.
Remember, the slope of a line is given by the formula:
slope = Δy / Δx
In this case, the Δy represents the change in position and Δx represents the change in time. Plugging in the values, we can calculate the slope (instantaneous velocity).
Once you have calculated the slope, you will have the instantaneous velocity at 8 seconds. Make sure to express the answer in units of meters per second (m/s) as required.
Note: If the position-time graph is not a straight line (i.e., if it is curved), finding the slope at a specific point becomes more complex. In such cases, calculus techniques are used to calculate the derivative and find the exact instantaneous velocity. However, for simpler cases, like a straight line, the method outlined above will work.