Yes, it is possible for both the initial velocity (u) and the final velocity (v) to be zero in certain scenarios. In physics, the change in velocity (∆v) is defined as the difference between the final velocity and the initial velocity (∆v = v - u). If both v and u are zero, then the change in velocity will also be zero (∆v = 0 - 0 = 0).
Here are a few examples where both u and v can be zero:
Projectile Motion at the Highest Point: When an object is launched vertically upward, its initial velocity (u) is positive, but at the highest point of its trajectory, the object momentarily comes to a halt. At that point, the final velocity (v) becomes zero before the object starts descending. Thus, both u and v are zero at the highest point.
Free Fall: If an object is dropped from rest (u = 0) and it falls freely under the influence of gravity, the initial velocity is zero. As it reaches the ground, the object comes to a stop before bouncing back up. At the highest point of the bounce, the final velocity is zero as well.
Inertia: In certain situations involving inertia, an object may be at rest initially (u = 0) and remains at rest throughout the entire motion. In such cases, both the initial and final velocities are zero.
It's important to note that while both u and v can be zero in these examples, there may be intermediate points where the velocities are different from zero. The key is that at specific moments or states, both the initial and final velocities can be zero.