A soccer player kicks a ball, giving it an initial velocity of 9.0 m/s in the positive x - direction. Because of the wet grass and dirt, the ball slows uniformly to 3.00 m/s when it has travelled 30.0 m. Determine the ball's acceleration? Hint: Acceleration is a vector and direction must be specified (SLO 1)

a = - 1.2 m/s²

Direction of a : in the negative x - direction

Explanation:

Because the ball moves with uniformly accelerated movement we apply the following formula:

vf²=v₀²+2*a*d Formula (1)

Where:

d:displacement in meters (m)

v₀: initial velocity in m/s

vf: final velocity in m/s

a: acceleration in m/s²

Known data

v₀ = 9.0 m/s

vf = 3.00 m/s

d = 30.0 m.

Problem development

We replace data in the formula (1) to calculate acceleration:

vf²=v₀²+2*a*d

(3) ² = (9) ² + (2 * 30) * a

9=81 + (60) * a

9-81 = (60) * a

-72 = (60) * a

a = - 72/60

a = - 1.2 m/s²

Direction of a : in the negative x - direction