The Velocity V(t)(t)= X'(t)at Time T of an Object Moving $x ^ { t } ( t ) = - 3 ( 3 t + 1 ) ^ { 1 / 2 }$

question 13

Multiple Choice

The velocity v(t) (t) = x'(t) at time t of an object moving along the x axis is given,along with the initial position x(0) of the object. $x ^ { t } ( t ) = - 3 ( 3 t + 1 ) ^ { 1 / 2 }$ ; x(0) = 4 Find:
(a) The position x(t) at time t.
(b) The position of the object at time t = 1.
(c) The time when the object is at x = 2.
Round answers for parts (b) and (c) to one decimal place.

• A)(a) \(x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 }\) (b)x(1)= -5.3(c)t = -0.3
• B)(a) \(x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 } + \frac { 14 } { 3 }\) (b)x(1)= 0.7(c)t = -7.7
• C)(a) \(x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 }\) (b)x(1)= 0.1(c)t = -12.3
• D)(a) \(x ( t ) = - \frac { 2 } { 3 } ( 3 t + 1 ) ^ { 3 / 2 } + \frac { 14 } { 3 }\) (b)x(1)= -0.7(c)t = 0.5

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Definitions:

Aleksandr Oparin

A Soviet biochemist known for his contributions to the theory that life on Earth developed through a process of chemical evolution.

Reducing Atmosphere

An atmospheric condition in which oxygen is scarce, favoring chemical reactions that reduce compounds.

Primitive Gases

Refers to the basic or primordial gaseous elements present in the earth's early atmosphere or in cosmic environments, often including hydrogen and helium.

Oxygen

A chemical element with symbol O, essential for respiration in most living organisms and required for combustion in fires.