How can an object (e.g. car) have zero velocity and nonzero (+/-) acceleration?

On top of this, how would this result in the object "speeding up?"

Answer 1

Imagine a circle.

Recall the velocity is displacement divided by time. So when you are going around in a circle, like a race track, you can be speeding up the whole way through but when you reach exactly where you started, your instantaneous velocity is #0m/s# as you displacement would be #0m# at that point.

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Answer 2

Olivia Askew

An object can have zero velocity and nonzero acceleration if it is changing its direction but not its speed. This occurs in circular motion when the object's velocity is constantly changing direction, causing its acceleration to be nonzero even when its speed remains constant.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.