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?
To find the initial acceleration and final velocity of the car, we need to use the formulas of motion.
Let's first assign some variables:
- Initial velocity (u) is the velocity of the car when it started accelerating.
- Final velocity (v) is the velocity of the car when it reached a constant velocity.
- Acceleration (a) is the rate at which the car's velocity is changing.
- Time taken to accelerate (t1) is the time it took the car to reach the constant velocity.
- Total time of the trip (t_total) is the time taken for the entire journey.
We can break down the problem into two parts:
1. The time taken to accelerate.
2. The time taken at constant velocity.
1. The time taken to accelerate:
We know that the car drove a total distance of 5 km during the entire trip. From the given information, we can find the distance covered during the acceleration phase using the formula:
Distance = Initial velocity * time + 0.5 * acceleration * time^2
The car starts from rest with an initial velocity of 0 km/h, so the equation simplifies to:
Distance = 0.5 * acceleration * time^2
Substituting the given values:
5 km = 0.5 * acceleration * (10 seconds)^2
2. The time taken at constant velocity:
We know the total time for the entire trip is 45 seconds. Therefore, the time taken at constant velocity is:
t2 = t_total - t1
Now we can solve for the initial acceleration (a) and final velocity (v) using the equations we derived above.
Solving Equation 1 for acceleration (a):
5 km = 0.5 * a * (10 seconds)^2
a = (2 * 5 km) / (10 seconds)^2
a = 1 km/s^2
Using Equation 2 to find the time at constant velocity (t2):
t2 = 45 seconds - 10 seconds
t2 = 35 seconds
Since the car is at a constant velocity during this time, the acceleration is 0 km/s^2, and we can use the equation:
v = u + a * t
Substituting the values:
v = 0 km/s + 0 km/s^2 * 35 seconds
v = 0 km/s
Therefore, the initial acceleration of the car is 1 km/s^2, and the final velocity is 0 km/s.