Show that these three forms of writing equations for oscillatory motion are equivalent. (the constant a in the first equation does not have to be the same as the constant a in the third equation)
x(t) = aei? t + be-i? t
x(t) = csin(? t) + dcos(? t)
x(t) = asin(? t + ? )

Initially, a particle is moving at 5.33 m/s at an angle of 37.9° above the horizontal. two seconds later, its velocity is 6.11 m/s at an angle of 54.2° below the horizontal. what was the particle's average acceleration during these 2.00 seconds in the x-direction (enter first) and the y-direction?

If the ama of the inclined plane below is 2, calculate the ima and efficiency. ima = efficiency =

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?