Question

A car accelerates uniformly from 12.5m/s at 10.0 degrees South of West to 105.0 m/s at 85.0 degrees South of West in 7.00 s. Determine the x and y components of the vehicles displacement. Determine the magnitude and direction of the vehicles displacement vector.

Answer 1

$v_2=v_1+at,$

$a=\frac{v_2-v_1}t=13.2~\frac ms,$

$|\Delta \vec v|=|\vec v_2-\vec v_1|=102.5~\frac ms,$

$l=\Delta v t=717.5~m,$

$\beta=75°+\arcsin(\frac{12.5}{102.5}\sin 75°)=82°$ south of east,

$l_x=l\cos82°=100~m,$

$l_y=l\sin 82°=710.5~m.$