Question

2). A particle moving on the x-axis has a time-dependent position (t) given by the equation x (t) = ct - bt^3. Where the units of x are meters (m) and time t in seconds (s). (Hint: you must get derivatives, you need graph paper)

(a) So that the position in x has units of meter which are the units of the constants c and b?

Sic = 5yb = 1.Desdeti = 0satf = 3s.

(b) What is its displacement, Δx?

(c) Graph position x vs. time for the following time values; t = 0s, 0.2s, 0.4s, 0.6s, 0.8s, 1s, 1.2s, 1.4s, 1.6s.

(d) Graph velocity v vs. time for the following time values; t = 0s, 0.2s, 0.4s, 0.6s, 0.8s, 1s, 1.2s, 1.4s, 1.6s.

(e) Describe the movement of this particle; using the following language how your position changes, how your speed changes and how your acceleration changes for the graphs of question (c) and (d).

Answer 1

Given:

a)

Since reads in metres and reads in seconds, the units of will be and unit of will be

b)

At , the position is at the origin and so the displacement is,

The value of unknowns are not given so that we cannot draw the graph for the same.