Abox is moving along the x-axis and its position varies in time according to the expression:
x = (6.00 m/s^2)t^2,
where x is in meters and t is in seconds.
(a) determine its position (in m) at t = 3.20 s.
(b) determine its position (in m) at t = (3.20 s) + δt.
(c) evaluate the limit of δx δt as δt approaches zero to find the velocity (in m/s) at t = 3.20 s.

Answers

The earths atmosphere is made up of nitrogen and oxygensolids turning into gases is called sublimation.
Learned about life itself

38.4 m/s

Explanation:

a) at t = 3.2s. x = 6 * 3.2^2 = 61.44 m

b) at t = 3.2 + Δt. x = 6*(3.2 + \Delta t)^2

c) As Δt approaches 0. We can find the velocity by the ratio of Δx/Δt

v = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{\Delta t}

v = \frac{6*(3.2 + \Delta t)^2 - 61.44}{\Delta t}

v = \frac{6(3.2^2 + 6.4\Delta t + \Delta t^2) - 61.44}{\Delta t}

v = \frac{61.44 + 38.4\Delta t + \Delta t^2 - 61.44}{\Delta t}

v = \frac{\Delta t(38.4 + \Delta t)}{\Delta t}

v = 38.4 + \Delta t

As Δt approaches 0, v = 38.4 + 0 = 38.4 m/s

38.4 m/s

Explanation:

a) at t = 3.2s. x = 6 * 3.2^2 = 61.44 m

b) at t = 3.2 + Δt. x = 6*(3.2 + \Delta t)^2

c) As Δt approaches 0. We can find the velocity by the ratio of Δx/Δt

v = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{\Delta t}

v = \frac{6*(3.2 + \Delta t)^2 - 61.44}{\Delta t}

v = \frac{6(3.2^2 + 6.4\Delta t + \Delta t^2) - 61.44}{\Delta t}

v = \frac{61.44 + 38.4\Delta t + \Delta t^2 - 61.44}{\Delta t}

v = \frac{\Delta t(38.4 + \Delta t)}{\Delta t}

v = 38.4 + \Delta t

As Δt approaches 0, v = 38.4 + 0 = 38.4 m/s



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