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A car is initially traveling west at 25 mph, and makes a turn north. As the car finishes the turn, its velocity is 20 mph north. It takes 3.5 seconds to complete the turn. What is the average acceleration of the car while it is turning, in mph/s?a. 0 -7.11+5.7.b. 7.1-5.73.c. 571-7.13.d. -5.7i+71.

Respuesta :

Answer:

a. -7.11+5.7

Explanation:

Given:

  • initial velocity of the car while travelling west, [tex]v_w=25\hat i\ mph[/tex]
  • velocity of the car after turning towards north, [tex]v_n=20\hat j\ mph[/tex]
  • time taken to turn, [tex]t=3.5\ s[/tex]

Now the acceleration:

[tex]a=\frac{v_w}{t} +\frac{v_n}{t}[/tex]

[tex]a=\frac{-25\hat i}{3.5} +\frac{20\hat j}{3.5}[/tex]

[tex]a=\frac{-50}{7} \hat i+\frac{40}{7} \hat j[/tex]

[tex]a=-7.1428\hat i+5.7142\hat j[/tex]

[tex]a=\sqrt{(\frac{50}{7} )^2+(\frac{40}{7} )^2}[/tex]

[tex]a=9.1473\ m.s^{-2}[/tex]

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