When a car of mass $1167 \mathrm {~kg}$ accelerates from 10.0 m/s to some final speed, 4.00 × 10⁵ J of work are done. Find this final speed. A)28.0 m/s B)22.4 m/s C)25.2 m/s D)30.8 m/s

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Quizplus · Accepted Answer

The work done on the car is equal to the change in its kinetic energy:$$W = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$where $m$ is the mass of the car, $v_i$ is the initial speed, and $v_f$ is the final speed.Solving for $v_f$, we get:$$v_f = \sqrt{\frac{2W}{m} + v_i^2}$$Plugging in the given values, we get:$$v_f = \sqrt{\frac{2(4.00 \times 10^5 \mathrm{~J})}{1167 \mathrm{~kg}} + (10.0 \mathrm{~m/s})^2} = 28.0 \mathrm{~m/s}$$

When a Car of Mass 1167 kg1167 \mathrm {~kg}1167 kg Accelerates from 10

When a Car of Mass $1167 \mathrm {~kg}$ Accelerates from 10