A freight train has a mass of 6.5 107 kg. If the locomotive can exert a constant pull of 11.5 105 N, how long would it take to increase the speed of the train from rest to 85 km/h?

s

netforce= totalmass*acceleration

find acceleration
then
vf=vi+at solve for t.

(change km/hr to m/s)

To find out how long it would take to increase the speed of the train from rest to 85 km/h, we can use Newton's second law of motion and the formula for acceleration.

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula is:

a = F/m

Where:
a = acceleration
F = net force
m = mass

In this case, the net force is given as 11.5 * 10^5 N, and the mass of the train is 6.5 * 10^7 kg. Plugging these values into the formula:

a = (11.5 * 10^5 N) / (6.5 * 10^7 kg)

Now, we need to convert the final speed from km/h to m/s. Since 1 km/h is equal to 1000 m/3600 s, the speed in m/s is:

85 km/h * (1000 m/3600 s) = 23.61 m/s

To find the time it would take to increase the speed to 23.61 m/s, we can use the formula for acceleration:

a = Δv / t

Where:
Δv = change in velocity
t = time

Initially, the train is at rest, so the initial velocity (v₀) is 0. Therefore, the change in velocity (Δv) is equal to the final velocity (v) of 23.61 m/s.

Plugging in the values:

23.61 m/s = a * t

Solving for t:

t = 23.61 m/s / a

Now, we can substitute the value of acceleration we calculated earlier:

t = 23.61 m/s / [(11.5 * 10^5 N) / (6.5 * 10^7 kg)]

Simplifying the expression:

t = 23.61 m/s * (6.5 * 10^7 kg) / (11.5 * 10^5 N)

t ≈ 131.32 s

Therefore, it would take approximately 131.32 seconds to increase the speed of the train from rest to 85 km/h.