The position of a particle moving along the x-axis depends on the time according to the equation x = ct2 - bt3, where x is in meters, t in seconds, and c and b are positive constants. what are the units of (a) constant c and (b) constant b? find a formula in terms of c, b, and t of the (c) velocity v and (d) acceleration a. (e) at what time t ≥ 0 does the particle reach its maximum x value?

(a):  

(b):  

(c):  

(d):  

(e):  

Explanation:

Given, the position of the particle along the x axis is

The units of terms and should also be same as that of x, i.e., meters.

The unit of t is seconds.

(a):

Unit of

Therefore, unit of

(b):

Unit of

Therefore, unit of

(c):

The velocity v and the position x of a particle are related as

(d):

The acceleration a and the velocity v of the particle is related as

(e):

The particle attains maximum x at, let's say, , when the following two conditions are fulfilled:

Applying both these conditions,

For ,

Since, c is a positive constant therefore, for ,

Thus, particle does not reach its maximum value at

For ,

Here,

Thus, the particle reach its maximum x value at time