An object travels North at 2 m/s for 9 s and then travels South at 4 m/s for 3 s. What are the object's average speed and velocity?

Jun 16, 2016

$\text{average speed :"v_a=2.5" } \frac{m}{s}$
$\text{average velocity :"v_a=1/3 " } \frac{m}{s}$

Explanation: $\text{the velocity of an object is defined as total distance covered in }$
$\text{unit time. Velocity is a scalar quantity. It has a magnitude but }$
$\text{no direction.}$

$\text{ average velocity of an object is calculated using formula:}$

${v}_{a} = \left(\text{total distance covered")/("given time interval}\right)$

$\text{figure 1 shows the distance of object P}$

"distance=AB+BC+CD+DE

$\text{northward :"x_N=2*9=18 " "m}$
$\text{southward :"x_S=4*3=12 " } m$

$\text{total distance covered: " x=18+12=30 " } m$
$\text{given time interval : "Delta t=9+3=12 " } s$
${v}_{a} = \frac{30}{12} = \frac{15}{6} = \frac{5}{2} = 2.5 \text{ } \frac{m}{s}$ $\text{Velocity is defined as net displacement of an object in unit time}$

$\text{Velocity is a vector quantity. it has both a magnitude and a direction}$

${v}_{a} = \left(\text{net displacement of object")/("time interval}\right)$

$\text{displacement is a vector quantity .}$

$\text{it is calculated either Pythagoras or cosine law} .$ $\text{net displacement="18-12=4" m}$

${v}_{a} = \frac{4}{9 + 3}$

v_a=4/12=1/3 " m/s