A train starts from rest from station P and accelerates uniformly for 2 minutes reaching a speed of 60 km/hr. It maintain this speed 10 minutes and then s uniformly for 3 minutes to comes to rest at station Q find;
a) The distance in PQ in km
b) The average speed of the train
c) The acceleration in m/s2.
step1:
v=0+2a=1, so a = 1/2 km/min^2
s=0+1/4*2^2=1
step2:
s=1*10
step3:
a = -1/3 km/min^2
s = 1*3 - 1/6 * 3^2 = 3/2
PQ = 1 + 10 + 3/2 = 25/2
avg speed = (25/2)/(2+10+3) = 5/6 km/min
there are two different accelerations, shown above. I assume you can convert to m/s^2
To find the answers to these questions, we can use the equations of motion.
a) The distance in PQ can be found using the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
In the first phase of motion, the train starts from rest, so the initial velocity is 0 m/s. The time is given as 2 minutes, which is 2 * 60 = 120 seconds. And we need to find the distance from station P to the point where the train reaches its maximum speed.
Using the equation, we can calculate the distance:
distance = (0 * 120) + (0.5 * acceleration * 120^2)
The acceleration is unknown, so we move to the second phase of motion. In this phase, the train maintains a constant speed of 60 km/h for 10 minutes, which is 10 * 60 = 600 seconds.
The distance covered during this phase is:
distance = 60 * 600 / 3.6 (converting km/hr to m/s)
Finally, in the third phase, the train s uniformly for 3 minutes, which is 3 * 60 = 180 seconds until it comes to rest at station Q.
Again, using the equation, we can calculate the distance:
distance = (0 * 180) + (0.5 * acceleration * 180^2)
Adding up the distances from the three phases, we get the total distance in PQ.
b) The average speed of the train can be calculated by dividing the total distance covered in PQ by the total time taken.
Total time = time taken in phase 1 + time taken in phase 2 + time taken in phase 3.
average speed = total distance / total time
c) The acceleration can be calculated using the equation:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is 0 m/s (stationary), and the final velocity can be found in phase 1 and phase 3. The time is already provided.
Now, let's calculate the answers step by step.