A car is moving with a velocity (3.0 m/s) € x ˆ + (1.0 m/s) € y ˆ and 3.0 seconds later its velocity is (6.0 m/s) € x ˆ - (3.0 m/s) € y ˆ. What is the direction of the average acceleration of the car?

-53.13°

Explanation:

Initial velocity, u = 3x + 1y

Final velocity, v = 6x - 3y

Time = 3s

To find acceleration, a:

a = (v - u) / t

a = [6x - 3y - (3x + y) ] / 3

a = (6x - 3y - 3x - y) / 3

a = (3x - 4y) / 3

a = x - 4/3y

To fine the direction, we use:

tanθ = y/x

tanθ = (-4/3 / 3) = (-4/3)

θ = - 51.13°