a freight train must approach a road crossing at 16km/h. after passing through the intersection, the train speeds up to 65 km/h, taking 10 min to do so. what is the train's acceleration during this time in meters per second squared

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To find the train's acceleration during this time, we need to convert the speed from km/h to m/s and calculate the acceleration using the formula:

Acceleration = (Final Speed - Initial Speed) / Time

First, let's convert the speeds to m/s:

Initial Speed = 16 km/h
Convert 16 km/h to m/s: (16 km/h) * (1000 m/km) / (60 min/h) / (60 s/min) = 4.44 m/s

Final Speed = 65 km/h
Convert 65 km/h to m/s: (65 km/h) * (1000 m/km) / (60 min/h) / (60 s/min) = 18.06 m/s

Time = 10 min
Convert 10 min to seconds: 10 min * 60 s/min = 600 s

Now, we can calculate the acceleration:

Acceleration = (18.06 m/s - 4.44 m/s) / 600 s = 0.0236 m/s²

Therefore, the train's acceleration during this time period is approximately 0.0236 m/s².

To find the train's acceleration during the time it takes to increase speed, we need to determine the change in velocity and the time it takes for this change.

First, let's convert the speeds from km/h to m/s. Since 1 km/h is equal to 0.2778 m/s, we have:

Initial speed (v1) = 16 km/h = 16 × 0.2778 m/s = 4.4444 m/s
Final speed (v2) = 65 km/h = 65 × 0.2778 m/s = 18.0555 m/s

Next, we need to convert the time taken for the velocity change from minutes to seconds. Since there are 60 seconds in a minute, 10 minutes is equal to 10 × 60 = 600 seconds.

Using the formula for acceleration (a) where a = (v2 - v1) / t, we can substitute the values to find the acceleration:

a = (18.0555 - 4.4444) / 600
= 13.6111 / 600
= 0.0226868 m/s²

Therefore, the train's acceleration during this time is approximately 0.0227 m/s².

(65-16)km/hr / 10min

= 4.9 (km/hr)/min
now, 1 km/hr = 1000m/3600s, so now you have

(4.9 * 1000/3600 m/s) / 60s
= 4.9*1000 / 60*3600 m/s^2