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Starting from rest, what is the shortest time this truck could accelerate uniformly to 38.0 m/s (≈ 85.0 mph ) without causing the box to slide. (Hint: First use Newton’s second law to find the maximum acceleration that static friction can give the box, and then solve for the time required to reach 38.0 m/s .)

Respuesta :

Answer:

[tex]t = 5.95 s[/tex]

Explanation:

As we know that the coefficient of static friction between box and the truck is given as

[tex]\mu_s = 0.65[/tex]

so the maximum static friction force on the box so that it will not slide on the truck is given as

[tex]F_f = \m_s mg[/tex]

so maximum possible acceleration of the box is given as

[tex]a = \mu_s g[/tex]

[tex]a = 0.65 (9.81)[/tex]

[tex]a = 6.38 m/s^2[/tex]

now time to reach the given speed is

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

[tex]38 = 0 + 6.38 t[/tex]

[tex]t = 5.95 s[/tex]

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