An object initially at rest experiences an acceleration of 1.4m/s2 for 8.0s and then travels at that constant velocity for another 6.0s . What is the object’s average velocity over the 14s interval?
first stage
v = a t = 1.4 * 8 = 11.2 m/s
x = .5 a t^2 = .7 * 64 = 44.8 meters
stage 2
Vi = 11.2
Xi = 44.8
a = 0
x = 44.8 + 11.2*6 = 112
went 112 meters in 14 seconds
112/14 = 8 meters/second average
To find the object's average velocity over the 14-second interval, we need to calculate the total displacement and divide it by the total time.
First, let's find the displacement during the first 8 seconds when the object experiences acceleration. We can use the equation:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the object is initially at rest (initial velocity = 0), the equation simplifies to:
displacement = 0.5 * acceleration * time^2
Substituting the values:
displacement = 0.5 * 1.4 m/s^2 * (8 s)^2
displacement = 0.5 * 1.4 m/s^2 * 64 s^2
displacement = 0.5 * 1.4 m/s^2 * 64 s^2
displacement = 44.8 m
During the next 6 seconds, the object travels at a constant velocity. Therefore, the displacement is just the product of the constant velocity and time:
displacement = velocity * time
displacement = 1.4 m/s * 6 s
displacement = 8.4 m
Now, to find the total displacement over the 14-second interval, we add the displacements during the acceleration phase and constant velocity phase:
total displacement = 44.8 m + 8.4 m
total displacement = 53.2 m
Finally, we can find the average velocity by dividing the total displacement by the total time:
average velocity = total displacement / total time
average velocity = 53.2 m / 14 s
average velocity = 3.8 m/s
Therefore, the object's average velocity over the 14-second interval is 3.8 m/s.
To calculate the average velocity of an object, we need to know both the total displacement and the total time.
First, let's find the displacement for each phase of motion:
Phase 1: The object experiences acceleration for 8.0 seconds.
Using the equation of motion: s = ut + 0.5at^2
where s is the displacement, u is the initial velocity (which is 0 since the object starts at rest), a is the acceleration, and t is the time.
s1 = (0 * 8.0) + 0.5 * 1.4 * (8.0^2)
s1 = 0 + 0.5 * 1.4 * 64
s1 = 0 + 0.5 * 89.6
s1 = 0 + 44.8
s1 = 44.8 meters
Phase 2: The object travels at a constant velocity for 6.0 seconds.
Since the object has a constant velocity, the displacement is given by the formula: s = vt
where s is the displacement, v is the velocity, and t is the time.
Since the velocity is constant, we can use the average velocity over the 8.0s interval, which is given to be 1.4 m/s^2.
s2 = 1.4 * 6.0
s2 = 8.4 meters
Now, let's calculate the total displacement by adding the displacement of each phase together:
Total displacement = s1 + s2
Total displacement = 44.8 + 8.4
Total displacement = 53.2 meters
Finally, we can calculate the average velocity using the displacement and total time:
Average Velocity = Total Displacement / Total Time
Total Time = 14.0 seconds (the sum of the times for both phases)
Average Velocity = 53.2 / 14.0
Average Velocity ≈ 3.8 m/s
Therefore, the object's average velocity over the 14s interval is approximately 3.8 m/s.