Easy Conceptual Kinematics Problem

[waters]

The acceleration of an object can be non-zero when the speed of the object is constant.

This is true. Why? If the velocity is constant, doesn't its derivative have a slope of 0?

 

[NewtonianAlch]

Think of an object with constant speed in a circular motion. Velocity is a vector quantity, consider those two ideas and see if you can understand it now.

 

[waters]

Thanks for the reply.

So it's true only because centripetal acceleration does not affect tangential velocity?

Is it true for objects in 1D? Because this statement is apparently true in all cases.

 

[NewtonianAlch]

You mentioned tangential velocity, that means it's got a direction associated with it right? So at any given point in a circular motion, the object that has constant speed is facing a new direction, so therefore what is also happening to the acceleration?

An object in 1D with constant speed in only one direction means what for the acceleration?

 

[waters]

I'm not too familiar with centripetal acceleration at all. But I'm assuming that the centripetal acceleration remains constant.

Does this count as 1D motion? If so, how?

 

[NewtonianAlch]

The magnitude of it would be the same yes, but remember these are vector quantities. If an object is moving in a circular motion, the direction is always changing because it's constantly facing a new direction, this is what tangential velocity refers to. So if it's repeatedly facing a new direction this must mean that the object is accelerating into a new direction, so therefore acceleration is not constant as the direction is always changing.

Movement in a circle is not 1 dimensional, it's 2 dimensional. Plot a circle on a graph, you will require both the x and y axis.

 

[NewtonianAlch]

I edited my earlier posts, I should have been saying constant speed! Not constant velocity, as speed is scalar, and velocity has direction, hope that's not confused you.