Answer:
The object can have zero velocity and, simultaneously, nonzero acceleration.
The object can have zero acceleration and, simultaneously, nonzero velocity.
The object can have nonzero velocity and nonzero acceleration simultaneously.
Explanation:
An object in simple harmonic motion has a total mechanical energy (sum of elastic potential energy and kinetic energy) that is constant:
E=U+K=1/2kx^2 + 1/2}mv^2
where,
k is equal to the spring constant
x is equal to the displacement
m is the mass
v is the speed
We can note that the force on the spring is given by Hook's law:
F=-kx
In Newton's law F = ma, this can be also be written as
ma=-kx
a=-k/mx
This implies that the acceleration is proportional to the displacement.
From the first equation, we can now states that:
When the displacement is zero, x=0, the acceleration is zero, a=0, and the velocity is maximum
When the velocity is zero, v=0, the acceleration is maximum, which occurs when the displacement is maximum
In all the other intermediate situations, both velocity and acceleration are nonzero.
So the correct answers are
The object can have zero acceleration and, simultaneously, nonzero velocity.
The object can have nonzero velocity and nonzero acceleration simultaneously.
The object can have zero velocity and, simultaneously, nonzero acceleration.
and 
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