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?

Answer 1

Answer:

4.15 m/s

Explanation:

Its given that acceleration is 0.1 m/s² with a direction opposite to the velocity. Since, the direction of acceleration is opposite to the velocity, this gives us a hint that the velocity is decreasing and so acceleration would be negative.

i.e.

acceleration = a = - 0.1 m/s²

Distance covered = S = 6m

Velocity after covering 6 meters = Final velocity = $v_{f}$ = 4 m/s

We need to find the initial speed, which will be the same as the magnitude of initial velocity.

Initial velocity = $v_{i}$ =  ?

3rd equation of motion relates the acceleration, distance, final velocity and initial velocity as:

$2aS = (v_{f})^{2}-(v_{i})^{2}$

Using the known values in the formula, we get:

$2(-0.1)(6)=(4)^{2}- (v_{i})^{2}\\\\ (v_{i})^{2}=16+1.2\\\\ (v_{i})^{2}=17.2\\\\ v_{i}=4.15$

Thus, the initial speed of the ball was 4.15 m/s