Analysis of Speed-Time Graphs: Constant and Uniformly Accelerated Motion

The diagram shows the speed-time graph of two objects \(A\) and \(B\) for the first \(10\) seconds of their motion.

Object \(A\) travels at a constant speed of \(12\) m/s throughout the \(10\) seconds.

Object \(B\) starts from rest, attains a speed of \(18\) m/s after \(4\) seconds and then travels at a constant speed.

1. Calculate
   1. the distance traveled by object \(B\) during the first \(4\) seconds of its motion.
   2. the average speed of object \(B\) for the first \(10\) seconds of its motion.
   3. the time taken for object \(B\) to travel at the same speed as object \(A\).
   4. the time taken for both to travel the same distance.
2. After \(10\) seconds, both objects slow down at the same rate until they come to rest.
   Given that object \(A\) comes to rest after a further \(6\) seconds, calculate the
   1. deceleration of object \(A\).
   2. total time taken for object \(B\) to travel the whole journey.