Answer:
The instantaneous speed of the object after the first five seconds is 12.5 m/s.
(C) is correct option.
Explanation:
Given that,
An object starts at rest. Its acceleration over 30 seconds.
We need to calculate the instantaneous speed of the object after the first five seconds
We know that,
Area under the acceleration -time graph gives speed.
According to figure,
Hence, The instantaneous speed of the object after the first five seconds is 12.5 m/s.
Answer:
a) The initial elastic potential energy of the block-spring system is 28.113 joules.
b) The final speed of the block is approximately 4.192 meters per second.
Explanation:
a) By applying Hooke's law and definition of work, we define the elastic potential energy (), measured in joules, by the following formula:
(1)
Where:
- Spring constant, measured in newtons per meter.
- Deformation of the spring, measured in meters.
If we know that and
, then the elastic potential energy is:
The initial elastic potential energy of the block-spring system is 28.113 joules.
b) According to the Principle of Energy Conservation, the initial elastic potential energy of the block-spring system becomes into translational kinetic energy, that is:
(2)
Where:
- Mass, measured in kilograms.
- Final speed, measured in meters per second.
Then, the final speed is cleared:
If we know that and
, then the final speed of the block is:
The final speed of the block is approximately 4.192 meters per second.