Final answer:
To find the dog's linear speed on the merry-go-round with a centripetal acceleration of 1.6 m/s² and a radius of 1.8 m, the formula v = sqrt(a * r) is used, resulting in a linear speed of 1.7 m/s.
Step-by-step explanation:
The student's question relates to calculating the linear speed of a dog sitting on a merry-go-round, with a given centripetal acceleration. The centripetal acceleration experienced by an object moving in a circular path is defined by the equation a = v^2 / r, where a is the centripetal acceleration, v is the linear speed, and r is the radius of the circle.
In this case, we have the centripetal acceleration a of 1.6 m/s² and the radius r of 1.8 m. To find the linear speed v, we rearrange the formula to v = sqrt(a * r) and substitute the given values to calculate v.
The calculation will be as follows:
v = sqrt(1.6 m/s² * 1.8 m)
v = sqrt(2.88 m²/s²)
v = 1.7 m/s
Therefore, the dog's linear speed is 1.7 m/s.