(a) assume the equation x = at3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

The dimension of A is L/T^3 and the dimension of B is L/T

Step-by-step explanation:

We can write the equation but just in terms of its dimensions and work with dimension analysis to find the dimensions of the constants.

Writing the dimensions equation.

For the given equation

We can write

We can then replace the dimensions where x is a length dimension which means and t has a time dimension, , so we get

Since we are adding terms on the right side both terms must have the same dimension. That means we have

And

Finding the dimensions of A and B

We can finally solve for the dimensions of each.

For A we have

Solving for [A] will give us

Solving for [B]

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value

step-by-step explanation:

4  

25

5258y

54.

t5

5r

54

5856

542

5458

86

.8558.65

565

565

55898

786

8/95

5896

8656265

556478