The throttle of an electric train is shut off at a speed of 48 km/h. The total mass of the train is 81

tonne and the combined resistance force is 90 newtons per tonne. Find how long it will take for the
train to stop.

To find out how long it will take for the train to stop, we need to calculate the deceleration of the train and then use it to find the stopping time.

First, let's convert the speed from km/h to m/s, as it is a more suitable unit for calculations:

48 km/h * (1000 m/1 km) * (1 h/3600 s) = 13.33 m/s

Next, we need to calculate the total resistance force acting on the train. The combined resistance force is given as 90 newtons per tonne, and the total mass of the train is 81 tonnes.

Total resistance force = Combined resistance force * Mass of the train
= 90 N/tonne * 81 tonne

To calculate the resistance force, we need to convert tonnes to kilograms:

Total resistance force = 90 N/tonne * 81 tonne * 1000 kg/tonne
= 7,290,000 N

Now, we can use the formula for deceleration to find the deceleration of the train:

Deceleration = (Final velocity - Initial velocity) / Time

Since the final velocity is 0 m/s (as the train is stopping), the deceleration formula can be rearranged as:

Deceleration = -Initial velocity / Time

Here, the initial velocity is 13.33 m/s, and we need to solve for time:

Deceleration = (-13.33 m/s) / Time

Substituting the calculated deceleration of the train:

(-13.33 m/s) / Time = 7,290,000 N / Total mass of the train

Now, let's substitute the values and solve for time:

(-13.33 m/s) / Time = 7,290,000 N / (81,000 kg)
Time * (-13.33 m/s) = (81,000 kg * 7,290,000 N)
Time = (81,000 kg * 7,290,000 N) / (-13.33 m/s)

Calculating this gives us:

Time = 44,887,768.9427 kg*N/s

However, we need to convert this back to a meaningful unit of time, such as seconds. To do this, let's divide by the force unit of N*s/kg (this unit is equivalent to m/s):

Time = 44,887,768.9427 kg*N/s / (N*s/kg)
Time = 44,887,768.9427 s

Therefore, it will take approximately 44,888 seconds for the train to stop.