I need help understanding when to use a negative sign for a final or initial vel

Question

I need help understanding when to use a negative sign for a final or initial velocity when solving for acceleration using the formula: a=(deltaV)/t. Example 1: If car is initially traveling at 100 m/s north, but it then traviling 80 m/s south 2 seconds later, what is the average acceleration. First, to find deltaV, I would do Vf-Vi. Would I do (-80 m/s)-(+100 m/s) or would i just find the displacement by doing (+100 m/s)-(+80 m/s)? Example 2: If a baseball is initially traveling at 70 mph and is then hit back at the pitcher with speed of 110 mph, to find deltaV, would I do (-110 mph)-(+70 mph) because the final velocity is traveling back towards pitcher or would I just do (+110 mph)-(+70 mph)?

Explanation / Answer

Velocity is a vector, therefore you need to define the directions with conventions. For example you need to use coordinate system to define the sign conventions.

For instance, consider north direction as positive Y direction and south direction as negative Y. The velocity in the north direction will be positive and in south it will be negative.

1: If car is initially traveling at 100 m/s north, but it then traveling 80 m/s south 2 seconds later, what is the average acceleration?

Average acceleration = Vf-Vi/Total time

Vf = -80 m/s

Vi = 100 m/s

a= -80-100/t

2 If a baseball is initially traveling at 70 mph and is then hit back at the pitcher with speed of 110 mph

Again define the directions, consider the ball out of pitcher as positive and coming to pitcher as negative

(-110 mph)-(+70 mph) = -180 mph

Divide it by total time, you will get the acceleration.

If the acceleration is negative that means it is in the direction of the acceleration is toward pitcher.

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