While travelling a distance of 27m the velocity of a train increased from 12m/sec to 54km/hr what is the uniform acceleration of the train.
54 km/hr = 15 m/s
Vfinal^2 - Vinitial^2 = 2 a X
81 m^2/s^2 = 2*a*27m
Solve for acceleration, a.
1,5
To calculate the uniform acceleration of the train, we need to use the formula:
acceleration (a) = (final velocity (v) - initial velocity (u)) / time (t)
However, we are not given the time taken to travel the distance of 27m. So we need to find the time first.
To find the time, we can use the equation:
distance (d) = (initial velocity (u) + final velocity (v)) / 2 * time (t)
Given:
distance (d) = 27m
initial velocity (u) = 12m/s
final velocity (v) = 54km/hr
First, let's convert the final velocity from km/hr to m/s:
54km/hr * (1000m/1km) * (1hr/3600s) = 15m/s
Now, we can substitute the given values into the equation to find the time:
27m = (12m/s + 15m/s) / 2 * t
27m = 27m/s * t
t = 27m / 27m/s
t = 1 second
Now that we have the time, we can calculate the acceleration using the initial and final velocities:
acceleration (a) = (final velocity (v) - initial velocity (u)) / time (t)
acceleration (a) = (15m/s - 12m/s) / 1s
acceleration (a) = 3m/s²
Therefore, the uniform acceleration of the train is 3m/s².