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 ___
the same as when it started from rest since
Δv=at=Ft/m
To determine the increase in the cart's speed when a constant force is exerted for a short time interval, we can use Newton's second law of motion.
Newton's second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass: F = ma, where F is the net force, m is the mass of the object, and a is the acceleration produced.
In this case, since the force is constant, we can rewrite Newton's second law as a = F/m. Since the mass of the cart remains constant, the equation simplifies to a = F/m.
If the cart is initially at rest, the initial velocity v0 would be 0. Therefore, the final velocity vf after the force is applied for the short time interval would be given by the equation:
vf = v0 + at
where a is the acceleration caused by the constant force and t is the time interval.
Now, let's consider the case where the cart is already moving with a constant speed in the direction of the force. This means that the initial velocity v0 is not 0. In this case, the equation for the final velocity becomes:
vf = v0 + at
Since the force is exerted for the same short time interval, the value of a and t remain the same as in the previous case. Therefore, the increase in the cart's speed when a constant force is applied for the same time interval would be the same, regardless of whether the cart was initially at rest or already moving with a constant speed.
So, the increase in the cart's speed would be the same in both scenarios.