an automobile manufacturer claims that its product will travel 0.5 km in 22 s, starting from rest. What is the magnitude of the constant acceleration required to do this?

The magnitude of the constant acceleration required to do this is 2.07 m/s²

Explanation:

Given;

distance the automobile will travel, d = 0.5 km = 500 m

initial velocity of the automobile, u = 0

time of travel, t = 22 s

Apply the following kinematic equation to determine the constant acceleration;

d = ut + ¹/₂at²

500 = 0 + ¹/₂(22)²a

500 = 242a

a = 500 / 242

a = 2.07 m/s²

Therefore, the magnitude of the constant acceleration required to do this is 2.07 m/s²

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west