The position versus time for a certain object

moving along the x-axis is shown. The object’s
initial position is −2 m. Find the instantaneous velocity at 6 s.
Answer in units of m/s

.

The instantaneous velocity at 6 s is 4 m/s.

To find the instantaneous velocity at 6 s, we need to calculate the derivative of the position function with respect to time. The derivative gives us the rate of change of position with respect to time, which is essentially the velocity.

Looking at the graph given, we can see that the position is a function of time. Let's denote the position as x(t), where t is the time.

In this case, the object's initial position is -2 m, so we can write the position function as:
x(t) = -2 + ...

Now, in order to find the remaining part of the equation, we need to examine the graph or any additional information provided. Unfortunately, since you have only mentioned the graph and not provided it, we don't have that information to complete the equation.

However, if you have knowledge of the graph or any further information about the object's position-time relationship, you can provide additional details, such as the equation of the graph or any specific points on the graph. With that information, we can proceed to find the instantaneous velocity at 6 s by taking the derivative of the position function with respect to time.

To find the instantaneous velocity at 6 seconds, we need to determine the slope of the position-time graph at that point.

From the graph, we can see that the object's initial position is -2 m. Therefore, it started at -2 m on the x-axis.

To calculate the instantaneous velocity, we need to find the change in position (∆x) over the given time interval (∆t). In this case, the time interval is 6 seconds.

Looking at the graph, we can see that at 6 seconds, the object's position is approximately 0 m.

∆x = 0 m - (-2 m) = 2 m
∆t = 6 s - 0 s = 6 s

Now, we can calculate the instantaneous velocity using the formula:

Instantaneous Velocity = ∆x / ∆t

Substituting the values:

Instantaneous Velocity = 2 m / 6 s = 1/3 m/s

Therefore, the instantaneous velocity at 6 seconds is 1/3 m/s.