An engine of mass 50,000 kg pulls a coach of mass 40,000 kg. If there is a resistance of 1 N per 100 kg acting on both the engine and the coach, and if the driving force of the engine be 4,500 N, then the acceleration of the engine is

The correct option is 0.08 m/s².

To find the acceleration of the engine, we can analyze the forces acting on the engine itself:

1. Identify the given parameters for the engine:
Mass of the engine ($m_{\text{engine}}$) = 50,000 kg
Driving force of the engine ($F_{\text{driving}}$) = 4,500 N
Frictional resistance rate = 1 N per 100 kg

2. Calculate the resistance force acting on the engine:
Since the resistance is 1 N for every 100 kg, the resistance force acting on the engine ($F_{\text{resistance}}$) is given by:
$F_{\text{resistance}}=\frac{\mathrm{50,000}}{100}\times 1=500\text{N}$

3. Calculate the net force acting on the engine:
The net force ($F_{\text{net}}$) acting on the engine is the driving force minus the resistance force:
$F_{\text{net}}=F_{\text{driving}}-F_{\text{resistance}}$
$F_{\text{net}}=\mathrm{4,500}-500=\mathrm{4,000}\text{N}$

4. Calculate the acceleration of the engine:
Using Newton's second law of motion ($F=ma$), the acceleration ($a$) is:
$a=\frac{F_{\text{net}}}{m_{\text{engine}}}$
$a=\frac{\mathrm{4,000}}{\mathrm{50,000}}=0.08{\text{m/s}}^2$

Thus, the acceleration of the engine is 0.08 m/s².