A car accelerates from 12m/s to 25m/s in 6.0s. What is its uniform acceleration? How far did it travel in this time?
acceleration = change in velocity/change in time
= 13/6 = 2.17 m/s^2
d = 0 + Vi t + (1/2) a t^2
= 12 (6) + 1.09 (36)
= 111 meters
another way is that if acceleration is constant, use average velocity
(12+25)/2 = 18.5 m/s
18.5 * 6 = 111 meters sure enough
Well, if a car accelerates from 12m/s to 25m/s in 6.0s, we can calculate its uniform acceleration by using the formula:
acceleration = (final velocity - initial velocity) / time
So, plugging in the values, we get:
acceleration = (25m/s - 12m/s) / 6.0s
Now, let's do some math here...
acceleration = 13m/s / 6.0s
Wait a second, I need to pause for comedic effect...
*dramatic pause*
So, the uniform acceleration of the car is approximately 2.1667 m/s².
Now, let's move on to the second part of the question, how far did it travel in this time?
To find the distance traveled, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time²
Since we're given the initial velocity, the time, and now we have the acceleration, we can calculate the distance.
distance = 12m/s * 6.0s + (1/2) * 2.1667m/s² * (6.0s)²
Let's do the math once again...
distance = 72m + (1/2) * 2.1667m/s² * 36.0s²
Wait for it...
*more comedic anticipation*
The distance traveled by the car is approximately 72m + 36.000m²/s².
So in conclusion, the car traveled a distance of approximately 108 meters in this time.
To find the uniform acceleration of the car, we use the equation:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity (u) is 12 m/s, the final velocity (v) is 25 m/s, and the time (t) is 6.0 s, we can substitute these values into the formula:
acceleration = (25 m/s - 12 m/s) / 6.0 s
acceleration = 13 m/s / 6.0 s
acceleration ≈ 2.1667 m/s² (rounded to four decimal places)
Therefore, the uniform acceleration of the car is approximately 2.1667 m/s².
To calculate the distance traveled, we use the equation:
distance = (initial velocity + final velocity) / 2 * time
Substituting the given values:
distance = (12 m/s + 25 m/s) / 2 * 6.0 s
distance = 37 m/s / 2 * 6.0 s
distance = 37 m/s * 6.0 s / 2
distance = 222 m / 2
distance = 111 m
Therefore, the car traveled a distance of 111 meters in this time.
To find the uniform acceleration of the car, we can use the formula:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity (u) is 12 m/s, the final velocity (v) is 25 m/s, and the time (t) is 6.0 seconds. Plugging those values into the formula:
acceleration = (25 m/s - 12 m/s) / 6.0 s
acceleration = 13 m/s / 6.0 s
acceleration = 2.17 m/s² (rounded to two decimal places)
So, the uniform acceleration of the car is approximately 2.17 m/s².
Next, to find how far the car traveled in this time, we can use another formula:
distance = (initial velocity + final velocity) / 2 * time
Plugging in the values:
distance = (12 m/s + 25 m/s) / 2 * 6.0 s
distance = 37 m/s / 2 * 6.0 s
distance = 37 m/s / 12.0 s
distance = 3.08 m/s (rounded to two decimal places)
Therefore, the car traveled approximately 18.33 meters in this time.