7. The rate at which the velocity of an object changes is the object's rate of acceleration.
8. Each second its speed increases by 8 m/s.
9. The distance the airplane travels each second is 8 m than the distance it traveled during the previous second
10. The ride's rate of acceleration during the 4 seconds is
Explanation:
7)
The acceleration of an object is defined as the rate of change in velocity of the object. Mathematically:
where
u is the initial velocity of the object
v is the final velocity
t is the time taken for the object's velocity to change from u to v
Acceleration is measured in meters per second squared (), and it basically gives a measure of how fast the velocity of an object changes.
Since velocity is a vector quantity, acceleration is a vector quantity as well: this means that an object is accelerated not only when its speed changes, but also when the direction of its velocity changes (for example, in a circular motion).
8)
The velocity of an object moving at constant acceleration is given by
where
u is the initial velocity
v is the velocity at time t
a is the acceleration
We can rewrite it as
where represents the change in velocity.
For the plane in this problem, its acceleration is
So, the change in velocity in a time of is
9)
The distance covered by an object moving at constant acceleration in a time is
where u is the velocity at the beginning of the time t considered, a is the acceleration, s is the distance covered.
So, the distance covered in a certain second is
After that second, the new velocity is
The distance travelled in the next second is
So, the difference in the distance travelled in the next second and in the previous second is
10)
The acceleration of the ride is given by
where
v is the final velocity
u is the initial velocity
t is the time interval
Here we have
u = 0 m/s
v = 40 m/s
t = 4 s
Substituting,
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