# An object travels North at 15 m/s for 2 s and then travels South at 2 m/s for 8 s. What are the object's average speed and velocity?

Sep 7, 2017

speed = 4.6 m/s
velocity = 1.4 m/s (north) or -1,4m/s (south)

#### Explanation:

To start of, we have to find the the total distance (or disposition covered) north and south which can be derived from the speed (or velocity) formula and total time taken
$s p e e d = \text{distance"/"time}$

therefore,
$\text{distance} = s p e e d \cdot t i m e$

When the object is traveling north:
$\text{distance} = 15 \cdot 2 = 30 m e t e r s$

When the object is traveling south
$\text{distance} = 2 \cdot 8 = 16 m e t e r s$

$T o t a l t i m e = 2 + 8 = 10 \sec o n \mathrm{ds}$

Now we have to distinguish between speed and velocity, since they are similar but they are not the same thing.

Speed is $\text{total distance covered" / "time}$

however,

Velocity is $\text{total disposition"/"time}$

Distance is not the same as disposition, as distance is a scalar quantity while disposition is a vector quantity.

Scalar quantities do not have direction, so the calculations are done without calculation,

$\text{distance} = 30 m e t e r s + 16 m e t e r s = 46 m e t e r s$
thus
$\text{speed"=46/10=4.6 "m/s}$

But, vector quantities are affected by direction, so we have to check the directions in calculations,

$\text{disposition"= 30 "meters (north)" -16 "meters (south)" = 14 "meters (north)}$ (the minus sign is because north is opposite direction to south)
thus,
$\text{velocity"=14/10=1.4 "m/s} \left(n \mathmr{and} t h\right)$

when calculated to south, the velocity will be $16 - 30 = - 14 \text{m/s south}$