A 3.9 kg particle starts from rest and moves a

distance of 2.4 m in 2.4 s under the action of
a single, constant force.
Find the magnitude of the force.
Answer in units of N.

A ship leaves its home port expecting to travel to a port 500.0 km due south. Before it moves even 1 km, a servere storm blows it 100.0 km due east. Hom far is the ship from its destination? In what direction must it travel to reach its destination?

X = (1/2) a t^2 = (1/2)(F/M)*t^2

X = 2.4 m is the distance it moves
a is the acceleration. which equals F/M
t = 2.4 s
Solve for F in Newtons

To find the magnitude of the force, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.

First, let's calculate the acceleration of the particle. We can use the formula:

acceleration = (final velocity - initial velocity) / time

Since the particle starts from rest, its initial velocity is 0. The final velocity can be calculated using the formula:

final velocity = initial velocity + acceleration * time

Given:
mass of the particle (m) = 3.9 kg,
distance (d) = 2.4 m,
time (t) = 2.4 s.

From the distance traveled, we can find the final velocity using the formula:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

2.4 m = 0 + (0.5 * acceleration * (2.4 s)^2)

Solving for acceleration:

acceleration = (2 * distance) / (time^2)
acceleration = (2 * 2.4 m) / (2.4 s)^2
acceleration = 2 m/s^2

Now, we can calculate the force using Newton's second law:

force = mass * acceleration
force = 3.9 kg * 2 m/s^2
force = 7.8 N

Therefore, the magnitude of the force acting on the particle is 7.8 N.

To find the magnitude of the force, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this case, we are given the mass of the particle (m = 3.9 kg) and the distance it moves (d = 2.4 m) in a certain time (t = 2.4 s).

First, we need to calculate the acceleration of the particle using the formula:

acceleration (a) = (change in velocity) / (time taken)

Since the particle starts from rest, its initial velocity (u) is 0. Therefore, we can calculate the change in velocity using the formula:

(change in velocity) = (final velocity) - (initial velocity) = (displacement) / (time taken)

Plugging in the values, we get:

(change in velocity) = (2.4 m) / (2.4 s) = 1 m/s

Now, let's calculate the acceleration:

acceleration (a) = (change in velocity) / (time taken) = 1 m/s / 2.4 s = 0.42 m/s²

Finally, we can calculate the magnitude of the force using Newton's second law:

force (F) = mass (m) × acceleration (a) = 3.9 kg × 0.42 m/s² = 1.638 N

Therefore, the magnitude of the force acting on the particle is approximately 1.638 N.