1. The Starship USS Enterprise is travelling in a straight flight path through the Delta Quadrant to investigate the Sontaran Nebula when its sensors detect a disturbance in the fabric of the space-time continuum. Captain Jean Luc Picard orders Lt. Commander Data to reverse course. However, as Data does this, the effect of the disturbance overtakes Enterprise.

Instantaneously, the crew and ship find themselves flying towards the point at which they detected this disturbance but from the opposite direction. Once again Captain Picard orders Data to reverse course and explain what has happened.

Data says, "Captain, my positronic circuits show that we have experienced a displacement phenomenon modelled by the mathematical function

s is our displacement in 1000s of km from the moment we detected the disturbance and t is the time elapsed in minutes. We are now back on course but displaced in parallel by 2000km."

(a) As Data reverses course the first time, Enterprise continues its forward motion for some minutes then returns the way it came. After how many minutes, correct to three significant figures, does Enterprise return to the point at which its sensors first detected the disturbance?

(b) After how many minutes does the effect of the disturbance overtake Enterprise?

(c) Data reverses course twice. Exactly when does Enterprise actually turn? Give your answers correct to three decimal places.

(d) What is the expression for the final course on which Enterprise is travelling?

(e) Data said, "We are back on course but displaced in parallel by 2000km". What was the original course and why does he say it is displaced by 2000?

(f) Captain Picard asks Data to display their displacement time graph on a monitor. Sketch and annotate what he would see for
0 ≤ t ≤ 10 and 0 ≤ s ≤ 34.

The nodes of a standing wave are points at which the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example, that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move).
Consider a standing wave

This question will strengthen your concepts of linear motion. A graph showing variation of velocity of a car moving along a straight line is given. You are required to find acceleration of the car at different moments of time and its displacement.

This graph is for understanding the concepts of variable velocity, uniform velocity, uniform acceleration, negative acceleration, displacement and average velocity of a body moving along a straight line.
Answer the following questions:
a. What is the velocity of the car at 2, 8, 16 and 20 s?
b. What is the acceleration of t

A woman walks at a constant rate for 10 seconds. For the next 5 seconds the woman speeds up to a run. After running at a steady rate for 5 more seconds, the woman stops for 5 seconds. It then takes the woman 5 seconds to run back to where she started. Graph the position of the woman as a function of time. Be sure to label your g

At time t = 0 s a hockey puck is moving with a velocity of 18 m/s.
It is decelerating at a rate of 0.95 m/s^2 (squared).
What displacement will the puck have in 1.5 s
Answer with number of meters rounded to the nearest whole number.
Thanks

An object is thrown downward from the top of a building with an initial velocity of 30 m/s. Assuming a positive direction of y measured downward from the top, derive an expression for (a) the velocity and (b) the displacement as a function of time. Assume y(0)=0

** Please see the attachment for the complete problem description **
A retarding force, symbolized by the dashdot in the figure to the right, slows the motion of the weighted spring so that the mass's position at time t is y = 22e^(-t) cos t, t >=0. Find the average value of y over the interval 0 < t < pi

I am unsure of how to properly answer this question.
What is the engine piston displacement in litres of an engine whose displacement is listed as 450 in.3? (inches cubed in.^3)
I made an attempt at the question:
450 in.3 (16.4 cm3 / 1 in.3 ) (1 mL / 1 cm3 ) ( 1 L / 1000 mL)
= 7.38 L
I'm not sure if that's right