Vector and Scalar

Quantities of Motion Motion can be thought of in either scalar quantities or in vector quantities. Scalar Quantities – values of amounts of motion with no regard for direction -- basically ask “how much?”, or “how far?” Vector Quantities – values of amounts of motion that include direction -- usually we represent the vectors as arrows

Comparing Scalar and Vector Quantities Scalar quantities are written very simply as an amount and a unit. Ex. 5 km, 250 m/s, 9.8 m/s2 Vector quantities are represented by an amount, a unit, and a direction. -- The direction is often represented by an arrow, and sometimes the length of an arrow is related to the amount of the quantity Ex. 5 km North, 250 m/s 9.8 m/s2

Adding Vector Quantities When adding vectors, we add up all of the vectors in one direction and subtract all of the vectors in the opposite direction. Ex. What is the total of the following vectors? a) b) 5 3 6 8 1 14 20 Answer: 8 (notice there is no negative sign. Vectors do not have to be negative to indicate direction) Answer: 3

Using Vector vs. Scalar Quantities Most of the time in this class, we will be more concerned with calculating the scalar quantity as opposed to the vector quantity. Often times, we know whether to use vector or scalar quantities by what the problem asks for. . . Problem Asks For: We Use: Distance Scalar Displacement Vector Speed Scalar Velocity Vector Acceleration Either one A good comparison of scalar vs. vector quantities is seen when we compare distance and displacement

More Difficult Distance/Displacement Problems Distance will always be easy to calculate, but most times, displacement isn’t in a straight line. It is then that you need to use the Pythagorean Theorem for triangles to figure out what your displacement is. Basically, this says that the hypotenuse (c) is related to the sides of the triangle (a and b), by the following equation: c2 = a2 + b2 We can, of course solve this equation for a, b, and c, but for displacement, we really only need to solve for c.

Example of a Difficult Problem A car started at point S below and drove to point E. What are its distance and displacement? 4 km S 3 km E