An object in space is initially stationary relative

to the Earth. Then, a force begins acting
on the object, starting with a force of 0 N, and
increasing at a uniform rate until the magnitude
of the force is 58 N after the force has
acted for 25 s. The body has a mass of 10 kg.
What is the speed of the object at 25 s?

Area under an F vs t curve is momentum. F is linear so we get a triangle:

.5 (58) 25 = 10 v
v = 72.5

Why did the object go to the party? Because it wanted to have a "force"-ful good time! *wink*

To calculate the speed of the object at 25 s, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, the force is increasing at a uniform rate.

So, let's find the acceleration first. Since the force starts at 0 N and increases to 58 N over 25 s, we can determine the average rate of increase:

Acceleration (a) = (final force - initial force) / time
= (58 N - 0 N) / 25 s
= 2.32 N/s^2

Now that we have the acceleration, we can calculate the speed using the formula:

Speed (v) = acceleration (a) * time (t)

Speed (v) = 2.32 N/s^2 * 25 s
= 58 m/s

So, the object will have a speed of 58 m/s at 25 s. Just in time to join the fun at the party!

To find the speed of the object at 25 seconds, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.

First, let's find the acceleration of the object. We know that the force acting on the object increases uniformly from 0 N to 58 N over a period of 25 seconds. So, the average force F average during this time is:

F average = (0 N + 58 N) / 2 = 29 N

Using Newton's second law, we can calculate the acceleration (a) as:

a = F average / mass
a = 29 N / 10 kg
a = 2.9 m/s^2

Next, we can use the equation for uniformly accelerated motion to find the final velocity (v) of the object:

v = u + a * t

where:
v is the final velocity,
u is the initial velocity (which is 0 m/s because the object is initially stationary),
a is the acceleration,
and t is the time.

Plugging in the values:

v = 0 m/s + (2.9 m/s^2) * 25 s
v = 0 m/s + 72.5 m/s
v = 72.5 m/s

Therefore, the speed of the object at 25 seconds is 72.5 m/s.

To find the speed of the object at 25 s, you 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.

First, let's calculate the acceleration of the object. We know that the force acting on the object increases uniformly until it reaches 58 N after 25 s. So we can find the average force during this time period by dividing the final force by the time taken:

Average force = final force / time = 58 N / 25 s = 2.32 N/s

Now, we can use Newton's second law to find the acceleration:

Force = mass x acceleration
2.32 N/s = 10 kg x acceleration

Solving for acceleration:
acceleration = 2.32 N/s / 10 kg
acceleration = 0.232 m/s²

Finally, we can use the equation of motion to find the speed of the object at 25 s. The equation for speed is:

speed = initial speed + acceleration x time

Since the object starts from rest (initially stationary), the initial speed is 0 m/s. Therefore:

speed = 0 m/s + 0.232 m/s² x 25 s
speed = 5.8 m/s

Hence, the speed of the object at 25 s is 5.8 m/s.