To solve this question, we need to understand the concept of impulse in physics.
Impulse (I) is defined as the change in momentum (Δp) of an object. Momentum (p) is a vector quantity that is the product of an object's mass (m) and its velocity (v), expressed as p = m v.
Now, impulse is related to the force (F) applied to an object and the time interval (t) over which this force is applied. The impulse-momentum theorem states that the impulse on an object is equal to the change in its momentum, which mathematically can be written as:
I = Δp
To find the change in momentum Δp, we can consider the initial momentum p_initial and the final momentum p_final of the object:
Δp = p_final - p_initial
Considering that a constant force is applied over a time interval (t), we know from Newton's second law that:
F = Δp / t
Rearranging this equation to solve for Δp gives us:
Δp = F t
If we substitute this back into the definition of impulse, we get:
I = Δp = F * t
Therefore, the correct equation for impulse is:
I = Δp = Ft
In the choices given, the only one that matches our equation is:
b. I = Δp = Ft
Thus, the correct answer to the question is choice b.
