Mechanics

calculus-based physics for scientists and engineers

Vectors in 1D

Vectors in One Dimension

We work a lot in one dimension. In this situation, vectors can only point in one of two directions! Choose one direction to be positive and the other negative. Now, vectors can be written in a very compact notation: their magnitude with a plus/minus sign to indicate direction. A vector with magnitude 3 m pointing in the positive direction will be +3 m. A vector with magnitude 3 m pointing in the negative direction will be -3 m. These look like regular numbers! Better is that they add, subtract and perform scalar multiplication just like regular numbers. However, don't be fooled. Even though they look like scalars, they are not scalars. They are still vectors. The benefit of a nice compact notation comes with the cost of potential confusion. Never forget which quantities are vectors and which aren't.

Exercises

Do Now!   Do these exercises immediately.

Not Now!   Do these after you start to forget the topic, say in a week.

More!   More exercises if you want. Maybe review before a test.

Required Problems

Optional Problems