An object initially at rest experiences an acceleration of 1.4 m/s² for 5.6 s then travels at that constant velocity for another 9.3 s. What is the magnitude of the object’s average velocity over the 14.9 s interval?
Why did the object go to the therapist? Because it couldn't find its average velocity!
But fear not, my friend, I'm here to help. Let's crunch some numbers, shall we?
The average velocity can be calculated by dividing the total displacement by the total time taken. In the first phase, the object experiences an acceleration, so we'll need to calculate its final velocity during that time.
Using the equation of motion, v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case since the object is at rest), a is the acceleration, and t is the time:
v = u + at
v = 0 + (1.4 m/s²) × (5.6 s)
v ≈ 7.84 m/s
Now that the object reaches a constant velocity of 7.84 m/s, we can calculate its overall displacement during phase two:
(displacement) = (velocity) × (time)
(displacement) = (7.84 m/s) × (9.3 s)
(displacement) ≈ 72.79 m
To find the average velocity, we divide the total displacement over the total time taken:
average velocity = (total displacement) / (total time)
average velocity = (72.79 m) / (14.9 s)
average velocity ≈ 4.89 m/s
So, the magnitude of the object's average velocity over the 14.9 s interval is approximately 4.89 m/s. Remember, speed isn't everything!
To find the magnitude of the object's average velocity over the 14.9 s interval, we need to calculate the average velocity for each segment separately and then take the magnitude.
First, let's calculate the average velocity during the period of acceleration. We can use the equation:
average velocity = (initial velocity + final velocity) / 2
Since the object is initially at rest, the initial velocity is 0 m/s. The final velocity during the period of acceleration can be calculated using the equation:
final velocity = initial velocity + (acceleration * time)
Plugging in the given values:
final velocity = 0 + (1.4 * 5.6) = 7.84 m/s
So, the average velocity during the period of acceleration is:
average velocity = (0 + 7.84) / 2 = 3.92 m/s
Next, let's calculate the average velocity during the period of constant velocity. Since the velocity is constant, the average velocity over this period is simply the velocity itself. The final velocity at this point is 7.84 m/s.
So, the average velocity during this period is:
average velocity = 7.84 m/s
To find the average velocity for the entire 14.9 s interval, we can calculate the weighted average of the velocities during the two periods. Since both periods have equal durations, we can take the simple average of the velocities.
average velocity = (3.92 + 7.84) / 2 = 5.88 m/s
Therefore, the magnitude of the object's average velocity over the 14.9 s interval is 5.88 m/s.
To find the magnitude of the object's average velocity over the 14.9 s interval, we need to calculate the total displacement and divide it by the total time.
Let's start by finding the displacement during the first phase when the object experiences an acceleration. We can use the formula for displacement:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the object is initially at rest, the initial velocity is 0, and the acceleration is 1.4 m/s². Plugging in these values, we get:
displacement = (0 * 5.6) + (0.5 * 1.4 * 5.6^2)
displacement = 0 + (0.5 * 1.4 * 31.36)
displacement = 21.952
Therefore, the displacement during the acceleration phase is 21.952 meters.
During the second phase, when the object travels at a constant velocity, the displacement is simply the product of the velocity and time:
displacement = velocity * time
The velocity during this phase is 1.4 m/s, and the time is 9.3 seconds. Plugging in these values, we get:
displacement = 1.4 * 9.3
displacement = 13.02
Therefore, the displacement during the constant velocity phase is 13.02 meters.
To find the total displacement over the 14.9 second interval, we add the displacements during the two phases:
total displacement = displacement during acceleration + displacement during constant velocity
total displacement = 21.952 + 13.02
total displacement = 34.972 meters
Now, we can calculate the average velocity by dividing the total displacement by the total time:
average velocity = total displacement / total time
average velocity = 34.972 / 14.9
average velocity ≈ 2.35 m/s
Therefore, the magnitude of the object's average velocity over the 14.9-second interval is approximately 2.35 m/s.
v = a t
v = 1.4 * 5.6
that is your constant velocity
x1 = (1/2) 1.4 (5.6)^2
that is where you are when you start your glide
x2 = x1 + v (9.3)
that is where you are at
t total = 5.6 + 9.3 = 14.9
avergae speed = x2/14.9