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A roller coaster starts at the top of a straight track that is inclined at 30degrees with the horizontal. This causes it to accelerate at a rate of 4.9m/s^2(1/2g).

a. What is the roller coaster's speed after 3 seconds?
b. How far does it travel during that time?

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Answer:

Part a)

[tex]v_f = 14.7 m/s[/tex]

Part b)

[tex]d = 22.05 m[/tex]

Explanation:

Part a)

Initial speed of the roller coaster

[tex]v_i = 0[/tex]

acceleration of the roller coaster is given as

[tex]a = 4.9 m/s^2[/tex]

now for the speed after 3 s is given as

[tex]v_f = v_i + at[/tex]

[tex]v_f = 0 + 4.9 \times 3[/tex]

[tex]v_f = 14.7 m/s[/tex]

Part b)

Distance traveled by the roller coaster

[tex]d = (\frac{v_f + v_i}{2})t[/tex]

[tex]d = (\frac{14.7 + 0}{2})(3)[/tex]

[tex]d = 22.05 m[/tex]

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