Final answer:
The acceleration of an object that accelerates uniformly from -6.90 m/s to +9.70 m/s over a distance of 3.20 m is calculated using the kinematic equation and results in an acceleration of 7.28 m/s^2.
Step-by-step explanation:
To calculate the acceleration of an object given its initial velocity, final velocity, and the distance over which it accelerates, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
- v is the final velocity,
- u is the initial velocity,
- a is the acceleration,
- s is the distance over which the acceleration occurred.
Given that the initial velocity u = -6.90 m/s, the final velocity v = +9.70 m/s, and the distance s = 3.20 m, we can rearrange the formula to solve for a:
a = (v^2 - u^2) / (2s)
Substituting the provided values into the rearranged formula:
a = (9.70^2 - (-6.90)^2) / (2 * 3.20)
After performing the calculations:
a = (94.09 - 47.61) / 6.40 = 7.28 m/s^2
The acceleration of the object is 7.28 m/s^2.