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A ball rolls across a floor with an acceleration of 0.100 m/s2 in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?a. 4.15 m/s.
b. 5.85 m/s.
c. 4.60 m/s.
d. 5.21 m/s.
e. 3.85 m/s.

Respuesta :

Lanuel

Answer:

a. 4.15 m/s.

Explanation:

Given the following data;

Acceleration, a = -0.100 because it's in the opposite direction.

Final velocity = 4

Distance = 6

To find the initial velocity of the ball, we would use the third equation of motion;

[tex] V^{2} = U^{2} + 2aS [/tex]

Where;

  • V represents the final velocity measured in meter per seconds.
  • U represents the initial velocity measured in meter per seconds.
  • a represents acceleration measured in meters per seconds square.
  • S represents the displacement measured in meters.

[tex] V^{2} = U^{2} + 2aS [/tex]

Making U the subject, we have;

[tex] U^{2} = V^{2} - 2aS [/tex]

Substituting into the equation, we have;

[tex] U^{2} = 4^{2} - 2*(-0.100)*(6) [/tex]

[tex] U^{2} = 16 + 1.2 [/tex]

[tex] U^{2} = 17. 2[/tex]

Taking the square root of both sides;

U = 4.147m/s ≈ 4.15m/s

Therefore, the initial speed of the ball is 4.15m/s.

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