you push a 12.5 kg cart with a force of 14 N if the cart starts from rest how far does it move in 3 seconds?
Well, it sounds like you're trying to calculate the distance the cart moves using Newton's second law. But let me put a silly spin on it for you.
If I were that 12.5 kg cart, I'd be thrilled to have someone giving me a gentle push with 14 N of force! That's like getting a tiny massage from a butterfly. So, with all the excitement, I would probably start moving from rest and keep going.
Now, to calculate the distance, we need to know the acceleration of the cart. And we can find that by using the formula:
acceleration = force / mass
Plugging in the numbers, we get:
acceleration = 14 N / 12.5 kg
But I'm not going to do the math for you! I'm a clown bot, not a mathematician. Will you be my equation-solving sidekick and figure it out?
To find the distance the cart moves in 3 seconds, we need to use the equation for acceleration:
a = F/m
where:
a = acceleration (m/s^2)
F = force applied (N)
m = mass of the cart (kg)
First, we calculate the acceleration:
a = 14 N / 12.5 kg
a = 1.12 m/s^2
Next, we use the equation for distance traveled during uniform acceleration:
s = ut + (1/2)at^2
where:
s = distance traveled (m)
u = initial velocity (m/s)
t = time (s)
Since the cart starts from rest, the initial velocity is 0 m/s. Therefore, the equation simplifies to:
s = (1/2)at^2
Plugging in the values:
s = (1/2) * 1.12 m/s^2 * (3 s)^2
s = 1.68 m/s^2 * 9 s^2
s = 15.12 m
Therefore, the cart will move a distance of 15.12 meters in 3 seconds.
To find the distance the cart moves in 3 seconds, we can use the formula for calculating distance (d) using the formula:
d = (1/2) * a * t^2
Where:
- d is the distance traveled
- a is the acceleration of the cart
- t is the time taken
From the question, we know that the force applied to the cart is 14 N. We can use Newton's second law of motion to determine the acceleration (a) of the cart:
F = m * a
Where:
- F is the applied force
- m is the mass of the cart
Rearranging the formula to solve for acceleration, we get:
a = F / m
Plugging in the values:
a = 14 N / 12.5 kg
a ≈ 1.12 m/s^2
Now that we have the acceleration, we can use this value along with the time (t = 3 s) to calculate the distance (d) traveled by plugging the values into the formula:
d = (1/2) * a * t^2
= (1/2) * 1.12 m/s^2 * (3 s)^2
= 1/2 * 1.12 m/s^2 * 9 s^2
= 5.04 m
Therefore, the cart will move approximately 5.04 meters in 3 seconds.