An electric train moving at 20kmh accelerates to a speed of 30kmh in 20s find the distance travelled in metres during period of acceleration
To find the distance traveled during the period of acceleration, you can use the formula:
distance = (initial velocity + final velocity) / 2 * time
First, let's convert the velocities from km/h to m/s, as the formula requires SI units.
Initial velocity = 20 km/h
Final velocity = 30 km/h
Time = 20 seconds
To convert km/h to m/s, you need to multiply the values by 1000/3600 (1 km = 1000 m, 1 h = 3600 s).
Initial velocity in m/s = 20 * (1000/3600) = 5.56 m/s
Final velocity in m/s = 30 * (1000/3600) = 8.33 m/s
Now we can substitute the values into the formula:
distance = (5.56 + 8.33) / 2 * 20
Calculating the numerator first:
5.56 + 8.33 = 13.89
Then dividing the numerator by 2:
13.89 / 2 = 6.94
Finally, multiplying by the time:
6.94 * 20 = 138.8 meters
Therefore, the distance traveled during the period of acceleration is 138.8 meters.