Asmall object moves along the xx-axis with acceleration ax(t)ax(t) = −(0.0320m/s3)(15.0s−t)−(0.0320m/s3) (15.0s−t). at tt = 0 the object is at xx = -14.0 mm and has velocity v0xv0x = 8.70 m/sm/s.

what is the xx-coordinate of the object when tt = 10.0 ss?

x = 54.3m (on the +ve x axis)

Explanation:

This is an Initial Value Problem. That means the initial values of certain parameters have been given and that can help solve the problem.

Given that acceleration, a, is:

ax(t) = - 0.032(15.0 - t)

And the initial values are:

x(t = 0) = - 14.0m

v(t = 0) = 8.7m/s

Hence,

a = - 0.032(15 - t)

a = - 0.48 + 0.032t

a = dv/dt = -0.48 + 0.032t

To obtain the velocity, v, integrate the acceleration and apply the initial values of v and t:

v = ∫dv/dt  = ∫(-0.48 + 0.032t)

∫dv = ∫(-0.48 + 0.032t)dt

(v - v₀) = -0.48(t - t₀) + 0.032(t²/2 - t₀²/2)

Inputting the initial values t₀ = 0s, v₀ = 8.7m/s:

=> v - 8.7 = -0.48t + 0.032t²/2

v = 8.7 - 0.48t + 0.016t²

To obtain distance, x, integrate the velocity and apply the initial values:

v = dx/dt = 8.7 - 0.48t + 0.016t²

=> ∫dx/dt = ∫(8.7 - 0.48t + 0.016t²)

∫dx= ∫(8.7 - 0.48t + 0.016t²)dt

(x - x₀) = 8.7(t - t₀) - 0.48(t²/2 - t₀²/2) + 0.016(t³/3 - t₀³/3)

Inputting the initial values t₀ = 0s, x₀ = - 14.0m:

(x + 14.0) = 8.7t - 0.48t²/2 + 0.016t³/3

x = 8.7t - 0.48t²/2 + 0.016t³/3 - 14.0

Now that the distance, x, has been obtained, when t = 10s:

x = 8.7*10 - 0.48*10²/2 + 0.016*10³/3 - 14.0

x = 87 - 24 + 5.3 - 14.0

x = 54.3m

Therefore, at time, t = 10s, x = +54.3m. (i.e. 54.3 on the +ve x axis).

need to see circuit to get time constant

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force