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The angle between the 2-m bar and the x-axis varies according to the equation = 0.3t3 - 1.6t + 3 where is in radians and t is in seconds. Which of the following most nearly gives the angular position of the bar when t = 2 s?
a. 126.05 b. 130.70 c. 112.15 d. 56.84​

Sagot :

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Answer:

a. 126.05

Explanation:

Equation

[tex]\theta = 0.3t^3 - 1.6t + 3[/tex]

Step-by-Step Solution:

1. Substitute ( t = 2 ) into the equation:

[tex]\theta = 0.3(2)^3 - 1.6(2) + 3[/tex]

2. Calculate each term separately:

[tex]( (2)^3 = 8 )[/tex]

[tex]( 0.3 \times 8 = 2.4 )[/tex]

[tex]( 1.6 \times 2 = 3.2 )[/tex]

3. Combine the terms:

[tex]\theta = 2.4 - 3.2 + 3[/tex]

4. Perform the addition and subtraction:

[tex]{\theta = 2.4 - 3.2 + 3 = 2.4 - 3.2 + 3 = -0.8 + 3 = 2.2}

[/tex]

The angular position

[tex]{ (\theta) \text when ( t = 2 ) seconds is ( 2.2 ) radians.}[/tex]

Conversion to Degrees:

To convert the angle from radians to degrees, use the conversion factor

[tex]( 180^\circ / \pi ):[/tex]

[tex]\theta_{\text{degrees}} = 2.2 \times \left( \frac{180^\circ}{\pi} \right)[/tex]

[tex]using \ (\pi \approx 3.14159):[/tex]

[tex]{\theta_{\text{degrees}} = 2.2 \times \left( \frac{180^\circ}{3.14159} \right) \approx 2.2 \times 57.2958 \approx 126.05^\circ}[/tex]