a train is moving at 30m/s when the brakes are applied the retardation is 2m/s (square). Find the velocity after 10sec and the time taken for train to come to rest
625m
Hdhs
To find the velocity after 10 seconds, we can use the equation:
v = u + at
Where:
v = final velocity (unknown)
u = initial velocity (30 m/s)
a = acceleration (retardation) (-2 m/s^2)
t = time (10 seconds)
Substituting the given values into the equation, we get:
v = 30 + (-2) * 10
v = 30 - 20
v = 10 m/s
Therefore, the velocity after 10 seconds is 10 m/s.
To find the time taken for the train to come to rest (velocity to be 0 m/s), we can rearrange the same equation:
v = u + at
Since the final velocity is 0, we get:
0 = 30 + (-2) * t
Rearranging the equation to solve for t, we get:
2t = 30
t = 30 / 2
t = 15 seconds
Therefore, the time taken for the train to come to rest is 15 seconds.
To find the velocity after 10 seconds, we can use the formula:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration (retardation in this case)
t = time
Given:
u = 30 m/s
a = -2 m/s^2 (negative sign represents the opposite direction)
t = 10 sec
Substituting the given values into the formula, we have:
v = 30 m/s + (-2 m/s^2) * 10 sec
To simplify, we can calculate the value inside the brackets first:
(-2 m/s^2) * 10 sec = -20 m/s
Now, we substitute this value back into the formula:
v = 30 m/s + (-20 m/s)
Adding these values, we get:
v = 10 m/s
Therefore, the velocity after 10 seconds is 10 m/s.
To find the time taken for the train to come to rest, we can use the same formula:
v = u + at
Since the final velocity (v) is 0 m/s when the train comes to rest, we can rearrange the formula to solve for time (t):
t = (v - u) / a
Substituting the given values into the formula, we have:
t = (0 m/s - 30 m/s) / (-2 m/s^2)
Simplifying the calculation inside the brackets:
(0 m/s - 30 m/s) = -30 m/s
Now, we substitute this value back into the formula:
t = (-30 m/s) / (-2 m/s^2)
Dividing these values, we get:
t = 15 sec
Therefore, the time taken for the train to come to rest is 15 seconds.