Question

If the car moves for equal times along the road and hill, create an expression for its average velocity vector v(ave) in terms of v0x, V1x, and v1y during the total time interval and unit vectors i and j

Answer 1

So here in order to find the average velocity we can say

$v_{avg} = \frac{displacement}{time}$

so first we know that along the horizontal and along the inclined it moves with same time interval

so here we will have displacement in x direction as

$x = v_o (t) + v_{1x}(t)$

now the average velocity in x direction will be given as

$v_{avg} = \frac{v_o t + v_{1x} t}{t + t}$

$v_{avg} = \frac{v_o + v_{1x}}{2}$

now similarly for y direction

first we will find its displacement

$y = v_{1y}(t)$

now the average velocity in y direction will be given as

$v_{avg} = \frac{v_{1y} t}{t + t}$

$v_{avg} = \frac{v_{1y}}{2}$

now net velocity is given as

$v_{avg} = \frac{v_o + v_{1x}}{2}\hat i + \frac{v_{1y}}{2}\hat j$