A motorist driving a 1200-kg car on level ground accelerates from 20.0 m/s to 30.0 m/s in a time of 5.0s. Neglecting friction and air resistance, determine the average mechanical power in watts the engine must supply during this time interval.
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A motorist driving a 1200-kg car on level ground accelerates from 20.0 m/s to 30.0 m/s in a time of 5.0s. Neglecting friction and air resistance, determine the average mechanical power in watts the engine must supply during this time interval.
Already answered elsewhere.
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To determine the average mechanical power the engine must supply, we can use the equation:
Power (P) = Work (W) / Time (t)
First, let's calculate the work done on the car during this time interval. The work done can be found using the formula:
Work (W) = Force (F) * Distance (d)
We know the mass of the car (m), the final velocity (vf), and the initial velocity (vi). From this information, we can calculate the force using Newton's second law:
Force (F) = mass (m) * acceleration (a)
To find the distance covered (d), we can use the formula for average velocity:
Average velocity = (initial velocity + final velocity) / 2
d = average velocity * time (t)
Now, let's plug in the values and calculate the average mechanical power:
Mass of the car (m) = 1200 kg
Initial velocity (vi) = 20.0 m/s
Final velocity (vf) = 30.0 m/s
Time (t) = 5.0 s
Calculations:
Acceleration (a) = (vf - vi) / t
a = (30.0 - 20.0) / 5.0
a = 2.0 m/s^2
Force (F) = m * a
F = 1200 kg * 2.0 m/s^2
F = 2400 N
Distance (d) = average velocity * t
d = ((20.0 + 30.0) / 2) * 5.0
d = 25.0 m
Work (W) = F * d
W = 2400 N * 25.0 m
W = 60000 J
Finally, we can find the average mechanical power (P):
P = W / t
P = 60000 J / 5.0 s
P = 12000 W
Therefore, the average mechanical power the engine must supply is 12000 watts.