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In these situations, you usually define one direction as being positive and the other as negative. In this problem, the question does this for us: it clearly tells us that when the ball is moving down the lane, its velocity is negative. "Down the lane" is the negative direction.

Average acceleration is give by

a_ave = Δv/Δt

where Δv is a change in velocity and Δt is elapsed time.

Δv = v_final - v_initial

In this problem, the ball "slowed down," but did not change direction. This means that the NUMBER associated with "v" got smaller (5 ... 4 ... 3 ...) but the SIGN (-) did not change.

I hope it makes sense, then, that "v_final" was a smaller (slower) number with a negative sign (moving down the lane) while "v_initial" was a larger (faster) number with a negative sign (moving down the lane).

The subtraction of a large negative number from a small one (like, for instance, -4 - [-10]) is a POSITIVE number whose value is given by the difference (+6).

So Δv is positive, and Δt is ALWAYS positive (no matter what).
Therefore a_ave, the quotient of two positive numbers, will be positive.

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Q: A bowling ball with a negative initial velocity slows down as it rolls down the lane toward the pins Is the bowling ball's acceleration positive or negative as it rolls toward the pins?
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