Question

A soccer ball is released from rest at the top of a grassy incline. After 8.6 seconds, the ball travels 87 meters and 1.0 s after this, the ball reaches the bottom of the incline. (a) What was the magnitude of the ball's acceleration, assume it to be constant

Answer 1

Answer:

a) a = 2.35 m/s^2

Explanation:

(a) In order to calculate the magnitude of the acceleration of the ball, you use the following formula, for the position of the ball:

$x=v_ot+\frac{1}{2}at^2$     (1)

x: position of the ball after t seconds = 87 m

t: time  = 8.6 s

a: acceleration of the ball = ?

vo: initial velocity of the ball = 0 m/s

You solve the equation (1) for a:

$x=0+\frac{1}{2}at^2\\\\a=\frac{2x}{t^2}$

You replace the values of the parameters in the previous equation:

$a=\frac{2(87m)}{(8.6s)^2}=2.35\frac{m}{s^2}$

The acceleration of the ball is 2.35 m/s^2