Final answer:
The rate of acceleration for the car that speeds up from 6 m/s to 20 m/s over a distance of 50 m is calculated using the formula a = (v² - u²) / (2s), which results in an acceleration of 3.64 m/s². The correct answer is option: 3.64 m/s²
Step-by-step explanation:
To determine the rate of acceleration of a car that changes its speed from 6 m/s to 20 m/s over a distance of 50.00 m, we can use the kinematic equations of motion. One such equation is:
v² = u² + 2as
Where:
v = final velocity (20 m/s)
u = initial velocity (6 m/s)
a = acceleration
s = distance traveled (50 m)
Rearranging the formula to solve for acceleration a, we get:
a = (v² - u²) / (2s)
Substituting the given values:
a = (20² - 6²) / (2 × 50)
a = (400 - 36) / 100
a = 364 / 100
a = 3.64 m/s²
Therefore, the rate of acceleration is 3.64 m/s².