Question

12. A runner at the start of a race generates 250 W of power as he accelerates to 5 m/s. If the runner has a mass of

60 kg, how long did it take him to reach that speed?

Answer 1

Using the work-energy principle, we can calculate that it took the runner 3 seconds to reach a speed of 5 m/s with a power output of 250 W, by equating the work done to the change in kinetic energy. It took the runner 3 seconds to reach the speed of 5 m/s.

Step-by-step explanation:

Calculating Time to Reach Speed with Power Output

To find out how long it took the runner to reach a speed of 5 m/s with a power output of 250 W, we'll need to use the work-energy principle. The work done by the runner is equal to the change in kinetic energy, which can also be expressed as power multiplied by time:

• Work (W) = Power (P) × Time (t)
• Kinetic Energy (KE) = 0.5 × Mass (m) × Velocity (v)2

As we are given the mass of the runner as 60 kg and the final velocity as 5 m/s, we can calculate the change in kinetic energy:
KE = 0.5 × 60 kg × (5 m/s)² = 0.5 × 60 × 25 = 750 J

Now, we know the power output of the runner is 250 W, so we can rearrange the formula to solve for time:
t = W / P = 750 J / 250 W = 3 s

Therefore, it took the runner 3 seconds to reach the speed of 5 m/s.

Answer 2

1/2 m/s2
30 Na




I hope this helps!