A constant force of 1.5 N to the right acts on a 2.5 kg mass for 0.30 s.

(a) Find the final velocity of the mass if it is initially at rest.
m/s to the right
(b) Find the final velocity of the mass if it is initially moving along the x-axis with a velocity of 12 m/s to the left.
m/s to the left

To answer this question, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

F = m * a

We can rearrange this equation to solve for acceleration:

a = F / m

Once we have the acceleration, we can use the following equation to find the final velocity of the object:

v = u + a * t

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time

Let's calculate the answers to the given question:

(a) Find the final velocity of the mass if it is initially at rest.

Given:
Force (F) = 1.5 N
Mass (m) = 2.5 kg
Time (t) = 0.30 s

Step 1: Calculate the acceleration (a):
a = F / m
a = 1.5 N / 2.5 kg
a = 0.6 m/s^2

Step 2: Calculate the final velocity (v):
u = 0 m/s (initial velocity)
v = u + a * t
v = 0 m/s + (0.6 m/s^2) * 0.30 s
v = 0 + 0.18 m/s
v = 0.18 m/s to the right

Therefore, the final velocity of the mass, if it is initially at rest, is 0.18 m/s to the right.

(b) Find the final velocity of the mass if it is initially moving along the x-axis with a velocity of 12 m/s to the left.

Given:
Force (F) = 1.5 N
Mass (m) = 2.5 kg
Time (t) = 0.30 s
Initial velocity (u) = -12 m/s (to the left)

Step 1: Calculate the acceleration (a):
a = F / m
a = 1.5 N / 2.5 kg
a = 0.6 m/s^2

Step 2: Calculate the final velocity (v):
v = u + a * t
v = -12 m/s + (0.6 m/s^2) * 0.30 s
v = -12 + 0.18 m/s
v = -11.82 m/s to the left

Therefore, the final velocity of the mass, if it is initially moving along the x-axis with a velocity of 12 m/s to the left, is 11.82 m/s to the left.