Question

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)

Answer 1

Answer:

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