(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.)[a] = = ) determine the dimensions of the derivative dx/dt = 3at2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)[dx/dt] =

A = [L*T^-3]

B = [L*T^1]

Explanation:

The equation

x = A*t^3 + B*t

has multiple terms that when added together result in x. We know x has dimension of length, so all the terms must have dimensions of length too.

A*t^3 = [L]

A*[T^3] = [L]

A = [L/T^3]

A = [L*T^-3]

And

B*t = [L]

B*[T] = [L]

B = [L/T]

B = [L*T^-1]

Heya!!

For this, let's start calculating aceleration magnitude with formula:

                                                  Δ   Being   Δ

                                              V = Final velocity

                                              Vi = Initial velocity

                                              t  = time

                                              a = Aceleration

⇒ Let's replace according the formula:

⇒ Resolving:

Now, we have the aceleration, so lets applicate second law of Newton for calculate net force applicated:

                                                  Δ   Being   Δ

                                                  F = Force

                                                  m = mass

                                                a = Aceleration

⇒ Let's replace according the formula:

⇒ Resolving:

Result:

The net force applicated is of -4,73 Newtons.

Extra:

The minus represents when the force acts in the opposite direction to the acceleration of the body.

Good Luck!!