Answer :
a) Yes, if acceleration and velocity have opposite directions
b) Yes, if acceleration and velocity have same direction
Explanation:
a)
In order to answer this question, we have to keep in mind that both velocity and acceleration are vector quantities, so they have also a direction.
Acceleration is defined as the rate of change in velocity:
[tex]a=\frac{v-u}{t}[/tex]
where
u is the initial velocity
v is the final velocity
t is the time elapsed
In this problem, the object is slowing down: this means that the magnitude of its velocity is decreasing, so
[tex]|v|<|u|[/tex]
This means that the direction of the acceleration is opposite to the direction of the velocity. Then, the magnitude of the acceleration can be increasing (this will not affect the fact that the object will slow down, but it will affect only the rate at which the object is slowing down).
b)
In this case, the object is speeding up. This means that the magnitude of its velocity is increasing, so we have
[tex]|v|>|u|[/tex]
In order for this to happen, it must be that the direction of the acceleration is the same as the direction of the velocity: therefore, this way, the magnitude of the velocity will be increasing (either in the positive or in the negative direction).
Then, the magnitude of the acceleration can be decreasing (this will not affect the fact that the object will speed up, but it will only affect the rate at which the object is speeding up).
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