Understanding Velocity and Acceleration: Scalar vs Vector Quantities

[venture]

are velocity and displacement vector quantities or scalar quantities?

if an object is going up is that when its acceleration is negative, and when that same object is coming back down does its acceleration become positive?

if a car is going downhill is its acceleration/velocity negative?

 

[bossman27]

are velocity and displacement vector quantities or scalar quantities?

They are definitely vector quantities, even though a lot of times in simple problems such as an object falling they might appear to be scalar since there's only one dimension in question.

if an object is going up is that when its acceleration is negative, and when that same object is coming back down does its acceleration become positive?

No, your confusing acceleration with velocity and then some. If you're talking about throwing a an object in the air, the acceleration is a constant. The acceleration is the rate of change of velocity, and is dependent only on Force. The force of gravity is constant, thus acceleration due to gravity is constant.
You can define the positive and negative directions whichever way you want, but when the object is going up the velocity is (positive or negative) and when it's falling back down, the velocity is the opposite sign.

if a car is going downhill is its acceleration/velocity negative?

This is a similar problem in which it totally depends on whether you define up or down to be positive. It really doesn't matter, as long as it's consistent throughout the problem.

 

[Angry Citizen]

are velocity and displacement vector quantities or scalar quantities?

Velocity is a vector. Displacement is a scalar, since it measures the distance from some origin.

if an object is going up is that when its acceleration is negative, and when that same object is coming back down does its acceleration become positive?

You can define your coordinate system in any way you choose. But acceleration is constantly pointed in whatever direction you consider "down", so long as no other force but gravity acts.

if a car is going downhill is its acceleration/velocity negative?

Again, you are a (budding) physicist here. The best thing about being a physicist is that you get to create the framework to solve the problem in whatever way you deem fit. You can define whatever coordinate system you want, so long as it is right handed and each direction is perpendicular to the other two directions. If you think it makes the math easier to say that a car going downhill has a negative y component, then that is your freedom. You can even define a coordinate system such that the car is not traveling downhill at all, but is instead moving along the axis you've defined. It may not necessarily be ideal to do so, but sometimes it can be. Point being, you have total freedom here, so both yes and no are correct answers.

 

[berkeman]

are velocity and displacement vector quantities or scalar quantities?

if an object is going up is that when its acceleration is negative, and when that same object is coming back down does its acceleration become positive?

if a car is going downhill is its acceleration/velocity negative?

Welcome to the PF, venture.

Please re-read the Rules link at the top of the page. You are supposed to show your own attempt at solving the questions befure you get tutorial help. Unfortunately, your homework has been done by a couple of our helpers this time...

 

[Nickie]

Velocity and displacement are both vector quantities because they have both magnitude and direction. This means that they can be represented by a vector, which includes both a numerical value and a direction.

When an object is moving upwards, its acceleration is typically negative because it is moving against the force of gravity. When the same object is coming back down, its acceleration becomes positive because it is moving in the same direction as the force of gravity.

Similarly, when a car is going downhill, its acceleration and velocity would typically be negative because it is moving against the direction of gravity. However, if the car is moving downhill but also accelerating in the same direction, its acceleration and velocity would become positive. It is important to consider both the direction of motion and the direction of acceleration when determining the sign of these quantities.