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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:

A. is equal to two times its initial speed.
B. is equal to the square of its initial speed.
C. is equal to four times its initial speed.
D. is the same as when it started from rest.
E. cannot be determined from the information provided.

Respuesta :

Answer:

d) is the same as when it started from rest

Explanation:

using equation of motion

v = u + at

second law of momentum defines

F = ma

a = F /m

the equation becomes

v = u + (F/m)t

from hear

since v is directly proportional to the force and the force remain the same, the increase in the cart speed will also remain the same.

After we exert the same constant force for the same short time interval, the increase in the cart's speed is;

Option D: Is the same as when it started from rest.

We are told that;

- the cart is initially at rest. Thus, u = 0 m/s

- A constant force is exerted for a short time interval

- The force gives the cart a certain final speed which we will call v.

Using Newton's first equation of motion, we have;

v = u + at

Where;

v is final speed

u is initial speed

a is acceleration

t is time

Since u = 0 m/s, we now have;

v = 0 + at

v = at

Now, from let us find a way to introduce force by the equation from Newton's second law of motion;

F = ma

Where;

F is force

m is mass

a is acceleration

Thus; a = F/m

Put F/m for a in v = at to get;

v = (F/m)t

We can see that the final speed v is directly proportional to the force. Thus, if the force remains the same, then the final speed will remain the same.

Read more about the relationship between force and velocity at; https://brainly.com/question/20137322

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