Calculate the average force an outside object would have to exert to bring a 1200-kg car to rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph). A)1.8 × 10⁴ N B)1.6 × 10⁴ N C)5.4 × 10⁴ N D)6.5 × 10⁵ N E)3.2 × 10⁴ N

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Quizplus · Accepted Answer

To find the average force, we can use the work-energy principle. The work done by the force is equal to the change in kinetic energy of the car. The initial kinetic energy (KE) of the car is given by $ \frac{1}{2}mv^2 $, where $ m = 1200 \, \text{kg} $ and $ v = 2.0 \, \text{m/s} $. The final kinetic energy is 0 (since the car comes to rest). The work done (W) is also equal to the force (F) times the distance (d), where $ d = 15 \, \text{cm} = 0.15 \, \text{m} $. Thus, we have:$$ W = \Delta KE = \frac{1}{2}mv^2 - 0 = \frac{1}{2} \times 1200 \times (2.0)^2 = 2400 \, \text{J} $$$$ W = F \times d $$$$ 2400 = F \times 0.15 $$$$ F = \frac{2400}{0.15} = 16000 \, \text{N} = 1.6 \times 10^4 \, \text{N} $$

Calculate the Average Force an Outside Object Would Have to Exert