(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]

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: