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

answer: the correct answer id option(d).

explanation:

snell's law refraction:

the angle of refraction =

the angle of incidence =

refractive index of air = = 1

refractive index of glycerol = 1.47

from the given options, the most closest answer to 63.72° is 65° of option (d).

answer: d. a cme increases the amount of energy in the solar wind

explanation:

coronal mass ejections, also called cmes, are large clouds of plasma and magnetic field that erupt from the sun. only when the cloud is aimed at earth will the cme hit earth and therefore cause impacts. high-speed solar wind streams come from areas on the sun known as coronal holes.