A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. Suppose we repeat the experiment but, instead of starting from rest, the cart is already moving with constant speed in the direction of the force at the moment we begin to apply the force.

After we exert the same constant force for the same short time interval, the increase in the cart’s speed
1. is equal to four times its initial speed.
2. is the same as when it started from rest.
3. cannot be determined from the information provided.
4. is equal to two times its initial speed.
5. is equal to the square of its initial speed.

2. it is the same as when it started from rest

The carts final speed is directly proportional to the force; since the force remained the same, so does the final velocity.

Bob stop being a stooge and get your stuff together pal. What on earth makes you think that IF you double the force, the final momentum thus velocity, is doubled.

Well, isn't this a paradoxical situation? It's like trying to catch up with a speeding train by running alongside it. No matter how hard you try, you'll never catch up! So, in this case, the increase in the cart's speed would be the same as when it started from rest, option 2. It's just one of those quirky physics things that keep us all on our toes!

To answer this question, we need to understand the concept of 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.

In this scenario, the cart is already moving with constant speed in the direction of the force when the force is applied. Since the cart is not at rest and has initial velocity, this means that the cart already has momentum.

When a constant force is exerted on an object for a short time interval, it causes a change in momentum of the object. The change in momentum can be calculated by multiplying the force applied by the time interval.

Since the force and time interval are the same in both scenarios (starting from rest and starting with initial speed), the change in momentum will be the same.

According to Newton's second law, the change in momentum is equal to the mass of the object multiplied by the change in velocity (final velocity - initial velocity).

Therefore, in both scenarios, the increase in the cart's speed will be the same, regardless of whether it started from rest or already had an initial speed. We can conclude that the answer is 2. The increase in the cart's speed is the same as when it started from rest.

IF you double the force, the final momentum thus velocity, is doubled.