motion in one dimension: confused about some stuff

[Chuquis]

Hello

 

I was cusrios to find out whether an objects velocity can be zero at the same instant that its acceleration is not zero. I am not confident about my answer which was pretty much a no and I gave an example about throwing ball in the air.

I was also not sure about a a question that said: if an object has a greater speed, does it necessarily have a greter acceleration. I answered yes and gave an example of a car but I am not confident of my answer.

 

I would really appreciate the help.

 

Thank you

[swansont]

Acceleration is the rate of change of velocity, and does not depend on the value of the velocity. The ball you threw will have v=0 at some particular time, when it reaches its apex, even though its acceleration is g throughout its path.

 

A car can have a constant large speed (say 100 kph = 62 mph), meaning that its acceleration is zero, while another can have a small speed but a nonzero acceleration, e.g. it started from rest.

[Amaton]

Hi Chuquis

 

If you're curious about what the subject is, take a look at rectilinear motion. Velocity is simply speed with direction. Since we only have two directions, we only indicate it by the number being positive or negative.

 

Think of acceleration as "how fast the velocity is changing". At any given point in time, it doesn't matter how big or how small the velocity is. Acceleration has to do with how much the velocity changes between given points in time. If you're going 10^23 km/h in the positive direction forever, then your acceleration is zero, because the velocity is not changing. Nonetheless, you're going insanely fast. Acceleration just measures change in velocity. Likewise, your actual speed at a given point in time doesn't depend on your acceleration at that same moment.

 

BTW, have you studied derivatives?

[Chuquis]

BTW, have you studied derivatives?

No I have not. Should I?

[Amaton]

No I have not. Should I?

 

It's not a necessity in this case, and it's totally fine if you haven't. But if you're interested, you can use this as a motivation to learn the topic.

 

Rectilinear motion in simple scenarios can be described with three functions of time: position, velocity, and acceleration -- all of which are related through the derivative. Knowing just one of these allows you to calculate either of them at any given point in time, which I think's pretty neat.