已知35公吨卡车的功率、速度变化及恒定阻力，求最大加速度

Let's break down how to solve this problem step by step—straightforward physics, no overcomplicating things:

Step 1: Calculate the constant total resistance force #

When the truck hits its maximum speed (65 km/h = 18.0556 m/s) at full 500kW power, its acceleration is zero. That means the engine's tractive force exactly balances the total resistance force (no net force acting on the truck).

We use the core power formula P = F * v, where P is power, F is force, and v is velocity. At max speed, the tractive force equals resistance (F = f), so rearrange to find resistance:
f = P / v_max

Plugging in the numbers:
f = 500000 W / 18.0556 m/s ≈ 27692 N

Step 2: Find the maximum possible tractive force #

Since the engine's power output is constant, tractive force and velocity are inversely proportional—the slower the truck moves, the more force the engine can deliver. That means the maximum tractive force occurs at the lowest given speed (50 km/h = 13.889 m/s).

Calculate this maximum force:
F_max = P / v_min
F_max = 500000 W / 13.889 m/s = 36000 N (this is exact: 50 km/h converts to 50/3.6 m/s, so 500000 / (50/3.6) = 500000 * 3.6 / 50 = 36000)

Step 3: Compute maximum acceleration with Newton's Second Law #

Newton's Second Law states F_net = m * a, where F_net is net force, m is mass, and a is acceleration. The net force here is the maximum tractive force minus the constant resistance force:
F_net = F_max - f

Plugging in our values:
F_net = 36000 N - 27692 N ≈ 8308 N

Now solve for acceleration:
a = F_net / m
a = 8308 N / 35000 kg ≈ 0.24 m/s²

So Stan's truck has a maximum acceleration of approximately 0.24 m/s².

内容的提问来源于stack exchange，提问作者Inquirer