This state of motionlessness occurs because all of the kinetic energy in the car is absorbed by the spring in the form of elastic potential energy. The mathematical representation is:
1/2 mv² = 1/2 kx²
25m = kx², where m is the mass of the cart, k is the spring constant and x is the spring's extension.
Acceleration = (change in speed) / (time for the change)
change in speed = (speed at the end) minus (speed at the beginning)
change in speed = (zero) minus (28 m/s) = -28 m/s
Acceleration = (-28 m/s) / (13 sec)
Acceleration = -2.15 m/s²
Answer: 90 kgm/s
Explanation:
The momentum (linear momentum)
is given by the following equation:
Where:
is the mass of the skater
is the velocity
In this situation the skater has two values of momentum:
Initial momentum: 
Final momentum: 
Where:


So, if we want to calculate the difference in the magnitude of the skater's momentum, we have to write the following equation(assuming the mass of the skater remains constant):
Finally:
Utilize the formula: 
= Final Velocity (86 m/s)
= Initial Velocity (0 m/s)
a = acceleration (m/s²)
t = Time (100 seconds)
As a result,
86 m/s = 0 + (a)(100 seconds)
Using algebra, divide 86 m/s by 100 seconds:
86 m/s = 100a
a = 0.86 m/s²
Rounded to one decimal place: 0.9 m/s²
Let me know if you have any questions!