Solving Kinematic Problems: A Car's Acceleration
In physics, kinematic equations are fundamental to understanding the relationship between velocity, acceleration, and distance. This article will demonstrate the application of these equations in a real-world scenario involving a car's acceleration. Specifically, we will solve for the car's new speed after a period of uniform acceleration.
Understanding the Problem
Consider a car traveling at an initial speed of 25 m/s. This car starts to accelerate uniformly at 3 m/s2 for a distance of 80 meters. The question is: what is the car's new speed after this period of acceleration?
Applying the Kinematic Equation
To solve this problem, we can use the following kinematic equation:
vi22vf22?2as
Where:
vvf is the final velocity (what we want to find) vvi is the initial velocity (25 m/s) a is the acceleration (3 m/s2) s is the distance (80 m)Step-by-Step Solution
First, we can plug in the values into the equation:
vvi2252?2·3·80
Calculating vvi2:
252625
Calculating 2·3·80:
2·3·80480
Now add these two results:
vvf2625?480145
Now, take the square root to find vvf:
vvf145
Therefore, the car's new speed is approximately 38.08 m/s.
Alternative Approach: Using SUVAT Equations
There are three SUVAT (uniformly accelerated motion) equations that can be used for solving this type of problem. The relevant equation here is:
vvf2vvi2 2as
Solving for vvf with the given values:
vvf2252 2·3·80
Calculating the values:
252625
2·3·80480
Adding these results:
vvf2625 4801105
Taking the square root to find vvf:
vvf1105approx 33.23 m/s
Therefore, the car's new speed is approximately 33.23 m/s.
Conclusion
By using the kinematic equations, we can accurately determine the new velocity of the car after a period of uniform acceleration. This problem involves a practical application of physics principles and demonstrates the utility of the SUVAT equations in solving real-world motion problems.