Answer:
It will take the train 8.2 min to reach a speed of 82 km/h
Step-by-step explanation:
Hi there!
Using Newton´s second law, we can calculate the acceleration of the train:
F = m · a
Where:
F = force exerted by the locomotive.
m = mass of the train.
a = acceleration of the train.
Solving the equation for the acceleration:
F/m = a
8.0 × 10⁵ N / 1.7 × 10⁷ kg = a
a = 4.7 × 10⁻² m/s²
Let´s convert 82 km/h to m/s:
82 km/h · (1000 m / 1 km) · (1 h /3600 s) = 23 m/s
Using the equation of velocity, we can calculate the time it takes for the train to reach a velocity of 23 m/s.
v = v0 + a · t
Where:
v = velocity at time "t".
v0 = initial velocity (in this case, v0 = 0 because the train starts from rest).
a = acceleration.
t = time.
23 m/s = 0 + 4.7 × 10⁻² m/s² · t
t = 23 m/s / 4.7 × 10⁻² m/s²
t =4.9 × 10² s
Let´s convert the seconds into minutes:
4.9 × 10² s · (1 min / 60 s) = 8.2 min
It will take the train 8.2 min to reach a speed of 82 km/h