A ball rolling with initial velocity of 40m/s(W) undergoes an acceleration of 5.0m/s^2(N) for a period of 6.0seconds.

(A) what is the final velocity of the ball?
(B) what is the displacement of the ball in the 6.0 sec

vf=vi+at

d=vi*t + 1/2 a t^2

To solve this problem, we can use the following kinematic equation:

vf = vi + at

where:
vf = final velocity of the ball
vi = initial velocity of the ball
a = acceleration
t = time

(A) To find the final velocity of the ball, we can substitute the given values into the equation:

vf = 40m/s + 5.0m/s^2 * 6.0s
= 40m/s + 30m/s
= 70m/s

Therefore, the final velocity of the ball is 70m/s.

(B) To find the displacement of the ball in the 6.0 seconds, we need to use another kinematic equation:

d = vit + 0.5at^2

where:
d = displacement of the ball
vi = initial velocity of the ball
a = acceleration
t = time

Since the initial velocity of the ball is in the west (negative), we'll use -40m/s for vi. Substituting the given values into the equation:

d = -40m/s * 6.0s + 0.5 * 5.0m/s^2 * (6.0s)^2
= -240m + 0.5 * 5.0 * 36.0
= -240m + 90m
= -150m

Therefore, the displacement of the ball in the 6.0 seconds is -150m, indicating that the ball has moved 150 meters to the west.

To find the final velocity and displacement of the ball, we can use the formulas of kinematics.

(A) Final velocity can be calculated using the formula:
Final velocity = Initial velocity + (Acceleration × Time)

Given:
Initial velocity (u) = 40 m/s (westward)
Acceleration (a) = 5.0 m/s^2 (northward)
Time (t) = 6.0 seconds

To simplify the calculations, let's assign a positive direction for eastward and northward. Since the initial velocity is westward, it will be negative. The acceleration is positive in the northward direction.

Substituting the values into the formula:
Final velocity = 40 m/s + (5.0 m/s^2 × 6.0 s)
Final velocity = 40 m/s + 30 m/s
Final velocity = 70 m/s (northward)

So, the final velocity of the ball is 70 m/s (northward).

(B) Displacement can be calculated using the formula:
Displacement = Initial velocity × Time + (1/2) × Acceleration × Time^2

Substituting the values into the formula:
Displacement = (40 m/s × 6.0 s) + (1/2) × (5.0 m/s^2) × (6.0 s)^2
Displacement = 240 m + (1/2) × 5.0 m/s^2 × 36.0 s^2
Displacement = 240 m + (1/2) × 5.0 m/s^2 × 1296 s^2
Displacement = 240 m + 10.0 m/s^2 × 1296 s^2
Displacement = 240 m + 12,960 m
Displacement = 13,200 m (northward)

So, the displacement of the ball in 6.0 seconds is 13,200 m (northward).