Final answer:
Using the kinematic equation v2 = u2 + 2as, the rate of acceleration of the car is found to be 3.75 m/s2, when it accelerates from 5.00 m/s to 20.0 m/s over a distance of 50.0 meters.
Step-by-step explanation:
In physics, when considering the motion of objects, we often need to calculate the rate of acceleration. In the scenario where a car accelerates from 5.00 m/s to 20.0 m/s over a distance of 50.0 meters, we can employ kinematic equations to find the acceleration. One such equation relates the squares of the speeds with the acceleration and the distance covered:
v2 = u2 + 2as,
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Now substituting the given values into the equation, we have:
20.02 = 5.002 + 2 · a · 50.0,
Solving for a gives us:
a = (20.02 - 5.002) / (2 · 50.0) = (400 - 25) / 100 = 375 / 100 = 3.75 m/s2.
The car's rate of acceleration is 3.75 m/s2.
This method of finding acceleration is fundamental in kinematics, a branch of physics dealing with the motion of objects without considering the forces that cause the motion.