A net force of 100 newtons is applied to a 20 kg cart that is already moving at 3 meters per second. The final speed of the cart was 8 m/s. For how long was the force applied?

F=ma

F=m(∆v/t)

Solving for timt (t):

t=(m∆v)/F

Where

t=?
m=20.0kg
∆v=8m/s-3m/s=5m/s
F=100N

Solve for t:

t=(20kg*5m/s)/100N

t=1s

I assume that the force was applied exactly in the direction of motion

change in momentum = 20(8-3)
= 100 kg m/s

Force = change in momentum /change in time
which is another way of saying F = ma

100 N = 100 kg m/s / change in time

so change in time = 1 second

Well, I guess the cart needed a bit of a push! It sounds like someone really wanted to get that cart moving faster. To calculate how long the force was applied, we need to use Newton's second law, which states that force equals mass times acceleration (F=ma).

In this case, we have a net force of 100 newtons being applied to a 20 kg cart. The acceleration of the cart can be found by calculating the change in speed (final speed minus initial speed) and dividing it by the time. So, we can write the equation as:

100 newtons = 20 kg × (8 m/s - 3 m/s) / t

Simplifying this equation, we have:

100 newtons = 20 kg × (5 m/s) / t

We can further simplify this equation to:

100 newtons = 100 kg m/s / t

Now, we can solve for t by dividing both sides of the equation by 100 kg m/s:

1 second = 1 kg m/s / (100 newtons)

So, the force was applied for 1 second. It seems like a short burst of force, but it was enough to give the cart a good speed boost!

To calculate the time for which the net force was applied, we need to 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. We can rearrange this equation to solve for acceleration:

F_net = m * a

Where:
F_net is the net force applied to the cart (100 N),
m is the mass of the cart (20 kg),
a is the acceleration of the cart.

Since the cart was initially moving and then changed its speed, we need to calculate the change in velocity (Δv). We can use the equation:

Δv = final velocity - initial velocity
Δv = 8 m/s - 3 m/s
Δv = 5 m/s

We can now calculate the acceleration using the formula:

a = Δv / t

Where:
a is the acceleration (unknown).
Δv is the change in velocity (5 m/s).
t is the time for which the force was applied (unknown).

Rearranging the equation to solve for time (t), we get:

t = Δv / a

Substituting the known values, we have:

t = 5 m/s / a

Now, substituting the value of acceleration (a) from Newton's second law into the equation and solving for time:

t = 5 m/s / (F_net / m)

t = 5 m/s / (100 N / 20 kg)

t = 5 m/s / (5 N/kg)

t = 1 second

Therefore, the net force was applied for 1 second to achieve the final speed of 8 m/s.