Question

What was the cart's instantaneous speed at 6 seconds? (Hint: Exactly at t=6)

Answer 1

1/2 m/s

Step-by-step explanation:

To solve for the instantaneous speed at t = 6 seconds, we need to look at the slope of the position-time graph at that exact point because the slope of a position-time graph gives us the velocity of the object at that point in time.

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In the graph you've provided, at t = 6 seconds, the graph shows a straight line segment which suggests constant velocity motion from about 5 seconds to 11 seconds. To find the slope (velocity) at t = 6 seconds, we can calculate the slope of the line segment between the points labeled B and C.

Using the slope formula:

`\text{Slope $(m)$}=(y_2-y_1)/(x_2-x_1)`

Where:

`\bullet \ (x_1,y_1) \rightarrow (5,-5) \\\\\bullet \ (x_2,y_2) \rightarrow (11,-2)`

Now solving:

`\Longrightarrow m=(-2-(-5))/(11-5)\\\\\\\\\Longrightarrow m=(3)/(6)\\\\\\\\\therefore \boxed{m=(1)/(2) \ m/s }`

Since speed is the magnitude of velocity and does not take into account direction, the instantaneous speed at t = 6 seconds is 1/2 m/s.