Final answer:
The acceleration of the ball as it rolls downhill, increasing speed from 6 km/hr to 3 m/s in 5 seconds, is 0.267 m/s².
Step-by-step explanation:
The question asks us to calculate the acceleration of a ball that increases in speed from 6 km/hr to 3 m/s over a period of 5 seconds. First, let's convert the initial speed from km/hr to m/s. Knowing that 1 km/hr is approximately 0.27778 m/s, we can calculate that 6 km/hr is equivalent to 6 × 0.27778 m/s = 1.66668 m/s. Now, we have both speeds in the same units.
The formula for acceleration is given by a = (vf - vi) / t, where 'vf' is the final velocity, 'vi' is the initial velocity, and 't' is the time taken. Substituting the values:
a = (3 m/s - 1.66668 m/s) / 5 s
= (1.33332 m/s) / 5 s
= 0.266664 m/s²
Therefore, the acceleration of the ball is 0.267 m/s² (rounded to three decimal places).