Particle Motion: Units of Constants, Maximum Position and Speed

[strugglin-physics]

The postiion of a particle able to move left or right along the x-axis is given by the function x(t) = ct^2 - bt^3, where c and b are constants. Your answers will be in terms of these two constants.

What are the units of c? What are the units of b?

What is the largest positive x position reached by this particle?

Does the particle reach a maximum speed (either positive or negative)? If so what is its maximum speed. If not, explain why not.


I know that the slope is the velocity, which is m/s but I don't know which one is the slope. As for the largest positive x position... I thought about maybe using the quadratic formula but the function is not really appropriately setup.

Any help would be appreciated.

 

[marlon]

The postiion of a particle able to move left or right along the x-axis is given by the function x(t) = ct^2 - bt^3, where c and b are constants. Your answers will be in terms of these two constants.

What are the units of c? What are the units of b?

since x is in m(etres) and t is in s(econds) a will have to be in : m/s²
b will have to be in m/s³

you know why ?

marlon

 

[marlon]

The postiion of a particle able to move left or right along the x-axis is given by the function x(t) = ct^2 - bt^3, where c and b are constants. Your answers will be in terms of these two constants.


What is the largest positive x position reached by this particle?

you have a function of which you need to know the maximum. Minima and maxima are called the extrema. These extrema can be calculated by taking the first derivative to t of the function x(t), and setting it equal to 0. You will get a quadratic formula and you need to solve this equation. This yields at best two different solutions. Just check out what solution corresponds to the maximum. There are several ways to do this. The most easy one is looking where the function is positive and negative...good luck

marlon