To find the force required to stop the Toyota Camry, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
First, we need to calculate the car's initial kinetic energy (KE_initial) when it's moving at a speed of 20 m/s:
\[ KE_{\text{initial}} = \frac{1}{2}mv^2 \]
Where:
- \( m = 1600 \) kg (mass of the car)
- \( v = 20 \) m/s (initial velocity of the car)
Now, substituting the values:
\[ KE_{\text{initial}} = \frac{1}{2} \times 1600 , \text{kg} \times (20 , \text{m/s})^2 \] \[ KE_{\text{initial}} = \frac{1}{2} \times 1600 \times 400 \] \[ KE_{\text{initial}} = 800 \times 400 \] \[ KE_{\text{initial}} = 320000 , \text{J} \]
Next, we want to stop the car, which means that the final kinetic energy (\(KE_{\text{final}}\)) will be 0 J.
The work done (W) to stop the car is equal to the change in kinetic energy:
\[ W = KE_{\text{final}} - KE_{\text{initial}} = 0 - 320000 = -320000 , \text{J} \]
The work done by the force is also given by the formula:
\[ W = F \cdot d \]
Where:
- \( F \) is the force.
- \( d \) is the distance over which the force is applied (100 m in this case).
We can rearrange this to solve for the force:
\[ F = \frac{W}{d} \]
Substituting the values we have:
\[ F = \frac{-320000 , \text{J}}{100 , \text{m}} \] \[ F = -3200 , \text{N} \]
The negative sign indicates that the force is acting in the opposite direction of motion (decelerating the car).
Thus, the force required to stop the Camry is 3200 N.
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