Problems of Velocity, Angular Velocity and Acceleration in Trains and Wheels

Question 1:

A train accelerates uniformly along a straight track and passes three trackside markers. The distance between the first two markers is equal to 0.25 km and between the second and third the distance is 0.4km. The train takes 26.6 seconds to travel between the first two markers and its speed as it passes the second marker is equal to 57.6 km/h.

Sketch the linear velocity-time diagram and calculate the following:

(a) the uniform rate of acceleration
(b) the time taken for the train to travel between the second and third markers
(c) the average velocity of the train for the journey between the first and third markers

Question 2:

An engine flywheel initially rotating at 24 rev/min is accelerated uniformly for 3.8 seconds whilst rotating through 41 revolutions. It is then immediately retarded at a uniform rate of 3.6 rad/s^2. The velocity of the flywheel is then held constant and finally decelerated uniformly at a rate of 1.4 rad/s^2 to a halt, this final deceleration taking place of 37 revolutions. The total time taken during these changes is equal to 2.1 minutes.

Sketch the linear velocity-time diagram for the flywheel and calculate the following

(a) the initial acceleration
(b) the maximum velocity reached
(c) the constant speed value
(d) the average angular velocity