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On a 150 m straight sprint, a cyclist accelerates from rest for 4.5 s at 3.8 m/s2. How long will it take her to complete the 150 m track, assuming she maintains her speed for the remaining part of the track?

Sagot :

whitneytr12

Answer:

It takes 6.52 s to complete the 150 m track.

Explanation:

Let's find the position of the cyclist during the acceleration.

[tex]x_{1}=v_{0}t+0.5at^{2}[/tex]

[tex]x_{1}=0.5(3.8)(4.5)^{2}[/tex]

[tex]x_{1}=38.48\: m[/tex]

Now, the final speed at this distance will be:

[tex]v_{f}=v_{0}+at[/tex]

[tex]v_{f}=3.8*4.5[/tex]

[tex]v_{f}=17.1\: m/s[/tex]

Now, we know that x(tot) = 150 m, the remaining part will be:

[tex]x_{2}=150-38.48=111.5\: m[/tex]

Therefore, the time is:

[tex]t=\frac{x_{2}}{V_{f}}[/tex]

[tex]t=\frac{111.5}{17.1}[/tex]

[tex]t=6.52\: s[/tex]

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