A car drove a total 5km. Accelerated 10seconds then had a constant velocity. Entire trip was 45 seconds. Was was the initial acceleration and final velocity?
During accleration, average speed was Vf/2. Vf is final velocity. Let's work with meters.
(Vf/2)*(10s) + Vf*35s = 5000 m
40 Vf = 5000
Vf = 125 m/s = 450 km/h
Initial acceleration = (125 m/s)/(10 s) = 12.5 m/s^2
The speed seems unrealistically high..
This would be near world record performance
http://www.youtube.com/watch?v=_pz3HE27bQg
To find the initial acceleration and final velocity, we need to analyze the given information about the car's motion.
Let's break down the information we have:
Total distance traveled (s) = 5 km
Time taken for the entire trip (t) = 45 seconds
Time taken to accelerate (t1) = 10 seconds
We can use the following kinematic equations:
1. Distance covered during acceleration (s1) = (1/2) * a * t1^2
2. Distance covered during constant velocity (s2) = v * (t - t1)
3. Total distance covered (s) = s1 + s2
From equation 1, we know that the distance covered during acceleration is given by:
s1 = (1/2) * a * t1^2
From equation 2, we know that the distance covered after acceleration during constant velocity is given by:
s2 = v * (t - t1)
From equation 3, we know that the total distance covered is given by:
s = s1 + s2
Combining these equations, we have:
5 km = (1/2) * a * (10 seconds)^2 + v * (45 seconds - 10 seconds)
Simplifying further, we get:
5 km = 50a + v * 35
This equation relates the initial acceleration (a) and final velocity (v) of the car. We can solve for these variables by rearranging the equation.
Since we have two unknowns, we need one more equation to solve this system. Let's consider the definition of velocity:
Velocity (v) = (Distance traveled) / (Time taken)
From the given information, we can calculate the average velocity of the car:
Average velocity = (Total distance traveled) / (Total time taken)
Average velocity = 5 km / 45 seconds
Now we have the second equation:
Average velocity = v
You can substitute this value for v in the first equation, resulting in a single equation with one unknown (a):
5 km = 50a + (5 km / 45 seconds) * 35
Now, you can solve this equation for 'a' by isolating it on one side of the equation and simplifying the calculations.