A child sits on the edge of a spinning merry-go-round that has a radius of 1.5 m. The childs speed is 2 m/s. What is the Child's acceleration?

2.66 m/s^2

a= v^2/r, directed inward

To find the child's acceleration, we need to use the formula for centripetal acceleration:

a = v^2 / r

Where:
a = acceleration
v = velocity
r = radius

Given:
v = 2 m/s
r = 1.5 m

Plugging in the values into the formula:

a = (2 m/s)^2 / 1.5 m

Simplifying the equation:

a = 4 m^2/s^2 / 1.5 m

a = 2.67 m/s^2

Therefore, the child's acceleration is 2.67 m/s^2.

To find the child's acceleration, we need to understand the relationship between acceleration, speed, and the radius of the spinning merry-go-round.

Acceleration is defined as the rate of change of velocity. In the case of circular motion, acceleration is directed towards the center of the circle and is called centripetal acceleration.

The formula for centripetal acceleration is given by:

a = v^2 / r

Where:
a is the centripetal acceleration,
v is the velocity of the object, and
r is the radius of the circle.

In this case, the child's velocity is given as 2 m/s and the radius of the merry-go-round is 1.5 m.

Plugging in these values into the formula, we get:

a = (2 m/s)^2 / 1.5 m

Simplifying the equation:

a = 4 m^2/s^2 / 1.5 m

a = 2.67 m/s^2

Therefore, the child's acceleration is 2.67 m/s^2.