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A car's engine has a power of 80 kW. What is the force exerted by the engine when the car is moving at a velocity of 32 m/s? (A) 1.50 x 103 N (B) 2.50 x 103 N (C) 3.00 x 103 N (D) 3.50 x 103 N

Physics

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Step-by-step solution

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B) 2.50×103 N2.50 \times 10^3 \text{ N}

  1. Identify the given values and the formula relating them.

    The power of the engine is P=80 kWP = 80 \text{ kW}.
    The velocity of the car is v=32 m/sv = 32 \text{ m/s}.
    The relationship between power (PP), force (FF), and velocity (vv) is given by:

    P=F⋅vP = F \cdot v
  2. Convert the power to standard SI units (Watts).

    P=80 kW=80×1000 W=80000 WP = 80 \text{ kW} = 80 \times 1000 \text{ W} = 80000 \text{ W}
  3. Rearrange the formula to solve for the force (FF).

    F=PvF = \frac{P}{v}
  4. Substitute the given values into the formula and calculate the force.

    F=80000 W32 m/sF = \frac{80000 \text{ W}}{32 \text{ m/s}} F=2500 NF = 2500 \text{ N}
  5. Express the force in scientific notation and compare with the given options.

    F=2.50×103 NF = 2.50 \times 10^3 \text{ N}

    This matches option B.

    The final answer is \boxed{\text{2.50 \times 10^3 N}}.

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