To find the tangential acceleration ($a_{\text{tangential}}$) of an object traveling in a circular path, we use the relationship:

$a_{\text{tangential}} = \alpha \cdot r$

Where:

• $\alpha$ is the angular acceleration in rad/s²
• $r$ is the radius of the circular path in meters.

Given in the problem:

• Angular acceleration $\alpha = 2.5 \, \text{rad/s}^2$
• Radius $r = 2.0 \, \text{m}$

Now, calculate the tangential acceleration:

$a_{\text{tangential}} = 2.5 \, \text{rad/s}^2 \times 2.0 \, \text{m}$

$a_{\text{tangential}} = 5.0 \, \text{m/s}^2$

So, the tangential acceleration is 5.0 m/s².

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. What is the difference between angular and tangential acceleration?
2. How does tangential acceleration affect the linear speed of an object?
3. What role does the radius play in determining tangential acceleration?
4. Can an object have tangential acceleration but no angular acceleration? Why or why not?
5. How would increasing the radius affect the tangential acceleration?

Tip: Remember, tangential acceleration only changes the speed along the circular path, not the direction. For directional changes, centripetal acceleration comes into play.