Question

Study the velocity vs. time graph. What is the displacement of the object from 2 seconds to 6 seconds?

1) 4 m
2) 8 m
3) 16 m
4) 24 m

Answer 1

The displacement of the object from 2 seconds to 6 seconds is 16 m (Option 3).

Step-by-step explanation:

To determine the displacement from the velocity vs. time graph, we can integrate the velocity function with respect to time over the given interval. Displacement (s) is the area under the velocity vs. time graph.

In this case, the graph shows a constant positive velocity of 4 m/s from 2 seconds to 6 seconds. The displacement (s) can be calculated using the formula:

`\[ s = \int_(2)^(6) v(t) \, dt \]`

Since the velocity is constant, this simplifies to:

`\[ s = v \cdot \Delta t \]`

Substitute the values
`(\(v = 4 \, \text{m/s}\)` and
`\(\Delta t = 6 - 2 = 4 \, \text{s}\))` into the formula:

`\[ s = 4 \, \text{m/s} \cdot 4 \, \text{s} = 16 \, \text{m} \]`

Therefore, the displacement of the object from 2 seconds to 6 seconds is 16 m, corresponding to Option 3.