A 100 kg object is moving at 5 m/s. If 50 N of force is applied to stop the object. How many meters does it take to stop the object? It takes _____ m to stop the object.

Answer 1

To find out how many meters it takes to stop the object, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.

1. Calculate the initial kinetic energy:
   The initial kinetic energy \( KE_i \) of the object can be calculated using the formula:
   \[ KE_i = \frac{1}{2} m v^2 \] where \( m \) is the mass and \( v \) is the velocity.
   Substituting the given values:
   \[ KE_i = \frac{1}{2} \times 100, \text{kg} \times (5, \text{m/s})^2 = \frac{1}{2} \times 100 \times 25 = 1250, \text{J} \]

2. Calculate the work done by the applied force:
   The work \( W \) done by the force to stop the object can be calculated using:
   \[ W = F \cdot d \] where \( F \) is the force and \( d \) is the distance. The work is also equal to the change in kinetic energy, which is:
   \[ W = KE_f - KE_i \] Since the final kinetic energy \( KE_f \) when the object is stopped is 0, we have:
   \[ W = 0 - 1250, \text{J} = -1250, \text{J} \]

3. Relate the work to the force and distance:
   Therefore, we can set up the equation:
   \[ -1250, \text{J} = 50, \text{N} \cdot d \] Solving for \( d \):
   \[ d = \frac{-1250, \text{J}}{50, \text{N}} = -25, \text{m} \]

Since distance cannot be negative in this context, we take the absolute value:
\[ d = 25, \text{m} \]

Thus, it takes 25 m to stop the object.