A car is traveling along a straight road at a velocity of +32.7 m/s when its engine cuts out. For the next 1.04 seconds, the car slows down, and its average acceleration is . For the next 5.23 seconds, the car slows down further, and its average acceleration is . The velocity of the car at the end of the 6.27-second period is +25.5 m/s. The ratio of the average acceleration values is = 1.36. Find the velocity of the car at the end of the initial 1.04-second interval.
To find the velocity of the car at the end of the initial 1.04-second interval, we can use the equations of motion.
The first step is to find the acceleration during the initial 1.04-second interval. We are given that the average acceleration during this interval is "a".
The average acceleration can be calculated using the formula:
average acceleration = change in velocity / time interval
Since the initial velocity is +32.7 m/s and the final velocity is unknown, we can write:
a = (final velocity - initial velocity) / 1.04
Next, we are given that the ratio of the average acceleration values is 1.36. We can set up the equation:
1.36 = (a2 / a1)
Let's assume the average acceleration during the second interval is a2 and during the first interval is a1.
Rearranging the equation above, we get:
a2 = 1.36 * a1
We are also given that in the next 5.23 seconds, the car slows down further, and its average acceleration is a2.
Using the equation of motion:
final velocity = initial velocity + (average acceleration * time)
For the first interval, the equation becomes:
final velocity1 = 32.7 + (a1 * 1.04)
And for the second interval, the equation becomes:
final velocity2 = final velocity1 + (a2 * 5.23)
We are given that the velocity of the car at the end of the 6.27-second period is +25.5 m/s, which corresponds to the final velocity2.
Substituting the known values into the equations, we can solve for a1 and find the velocity of the car at the end of the initial 1.04-second interval.