Final answer:
To find the constant acceleration of a vehicle that changes its velocity from 40 m/s to 80 m/s over a distance of 200 m, one can use the kinematic equation v² = u² + 2as, which yields an acceleration of 12 m/s².
Step-by-step explanation:
To calculate the constant acceleration of a vehicle that changes its velocity from 40 m/s to 80 m/s over a distance of 200 m, we can use the following kinematic equation:
v² = u² + 2as
Where v is the final velocity (80 m/s), u is the initial velocity (40 m/s), a is the acceleration, and s is the distance over which the acceleration occurs (200 m)
Rearranging the formula to solve for a:
a = (v² - u²) / (2s)
Plug in the values:
a = (80² - 40²) / (2 × 200)
After calculation:
a = (6400 - 1600) / 400a = 4800 / 400a = 12 m/s²
Therefore, the constant acceleration of the vehicle is 12 m/s².