The position of a particle moving along the x axis depends on the time according

Question

The position of a particle moving along the x axis depends on the time according to the equation x = ct^2 - bt^3, where x is in meters and t in seconds.For the following, let the numerical values of c and b be 3.9 and 1.0, respectively. (For vector quantities, indicate direction with the sign)

a) At what time does the particle reach its maximum positive x position?

b) From t = 0.0 s to t = 4.0 s, what distance does the particle move?

c) From t = 0.0 s to t = 4.0 s, what is its displacement?

d) Find its velocity at t = 1.0 s

e) Find its velocity at t = 2.0 s.

f) Find its velocity at t = 3.0 s

g) Find its velocity at t = 4.0 s

h) Find its acceleration at at t = 1,2,3, & 4.0 s

Explanation / Answer

reat c and b as velocities. You can find simple ways to show this.

x = c ( 4 + t3 ) - b ( t3 )
= 15.6 + 3.9 t3 - 1.0 t3
= 15.6 + 2.9 t3

x = c ( t2 ) - b ( t2 - 4 )
= 3.9 t2 - t2 + 4.0
= 2.9 t2 + 4.0

15.6 + 2.9 t3 = 2.9 t2 + 4.0
2.9 ( t2 - t3 ) = 15.6 - 4.0
2.9 ( 4.0 ) = 11.6

Your displacement is 11.6

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