The position of a particle change is literally with time, I.e. as one power of t, as given by the following: h(t) =(3.3 t + 6.3) meters. Find the speed of the particle in meters per second

Consider a non-stationary time series is defined as below Yt = B0 +B1t+et Where et is error term and IID in nature. Prove that 1st difference of this series is stationary.

A piece of wood moves at a velocity (measured in millimeters per year) of v(1) = r² – 3t – 4 where 1 = 1 would be the end of the first year. If a is the displacement of the wood in the first 5 years and b is the distance traveled in the first 5 years, what is a- b? None of the listed answers

The instantaneous speed of a particle moving along one straight line isv(t) = ate−5t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)

An object's velocity as a function of time in one dimension is given by the expression; v(t) =  3.8t + 6.68 where are constants have proper SI Units. At what time is the object's velocity 61.2 m/s?

In the answer, it gives a formula f-ff=m(0) and afterwards simplies into 120 - ff = 0 and further into ff=120N. My question is how do you not have to divide by 0 to finish the equation if that makes sense. To simply further why are we able to ignore the m(0) portion?

A particle of mass m has a time-dependent position vector r(t) = (Rcos(ωt),Rsin(ωt),αt) in Cartesian coordinates, where R, ω and α are positive constants. What are the physical dimensions of R, ω and α? Show that the speed of the particle is constant. Does it mean that the acceleration is zero? Justify.

A vector is given by: i = (-2.11) + ( -4.28) ĵ+ ( 2.8 ) k. Determine the component of the unit vector û .

Part (a)  Do this for the range r > R.  E = _____ Part (b)  Do this for the range r < R.  E = _____

For vectors A= -3i + 7j - 8k and B = - 4i - 7j + 10k, find the scalar component of B along  A