Question

A train enters a curved horizontal section of track at a speed of 100km/h and slows down with constant deceleration to 50km/h in 12 seconds. An accelerometer mounted inside the train records a horizontal acceleration of 2meter/second square when the train is 6 seconds into the curve. Calculate the radius of curvature p of the track for this instant.

Answer 1

To calculate the radius of curvature of the track, use the formula r = v^2 / (a - g), where v is the velocity of the train, a is the horizontal acceleration of the train, and g is the acceleration due to gravity. Substitute the given values into the formula to find the radius of curvature.

Step-by-step explanation:

To calculate the radius of curvature of the track at the instant when the train is 6 seconds into the curve, we need to use the formula:

r = v^2 / (a - g)

Where:

• r is the radius of curvature of the track
• v is the velocity of the train
• a is the horizontal acceleration of the train
• g is the acceleration due to gravity

Given that the train enters the curve with a speed of 100 km/h (27.8 m/s), slows down to 50 km/h (13.9 m/s) in 12 seconds, and has a horizontal acceleration of 2 m/s^2, we can substitute these values into the formula to find the radius of curvature:

r = (27.8^2) / (2 - 9.8) = 400.96 m

Therefore, the radius of curvature of the track at that instant is 400.96 meters.