Question

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.

Answer 1

a. 4.15 m/s.

Step-by-step 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;

`V^(2) = U^(2) + 2aS`

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.

`V^(2) = U^(2) + 2aS`

Making U the subject, we have;

`U^(2) = V^(2) - 2aS`

Substituting into the equation, we have;

`U^(2) = 4^(2) - 2*(-0.100)*(6)`

`U^(2) = 16 + 1.2`

`U^(2) = 17. 2`

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.