Question

You notice a one-dimensional-thinking snail crawling along one rail of a railroad track. Naturally, you move it to a safer place. But before you do, you observe it as it moves from position xi=−97.9 cm to position xf=−64.7 cm along the rail, as measured from a nearby joint between two segments of rail. What is the snail's displacement Δx in centimeters?

Answer 1

• The displacement is 33.2 cm in direction to the joint.

Step-by-step explanation:

The displacement can be obtained as the vector pointing from the starting position to the final position. The nearby joint give us an frame of reference. Putting the starting of the coordinate system at the nearby joint, the vector for the starting position is:

`\vec{x}_i =  -97.9 \ cm  \ \hat{i}`

where
`\hat{i}` is the unit vector pointing from this position to the joint. The final position is:

`\vec{x}_f =  -67.4 \ cm \ \hat{i}`.

So, the displacement vector
`\vec{D}` will be

`\vec{D} = \vec{x}_f - \vec{x}_i`

`\vec{D} = -67.4 \ cm \ \hat{i} - (-97.9) \ cm \ \hat{i}`

`\vec{D} = -67.4 \ cm \ \hat{i} + 97.9 \ cm \ \hat{i}`

`\vec{D} = 33.2 \ cm \ \hat{i}`

This is 33.2 cm pointing to the joint.