A resting car starts accelerating with #α=5.0m/s^2# , then uniformly, and finally, decelerating at the same rate, #α#, comes to a stop. The total time of motion equals #t=25s#. The average velocity is #72# kmph. For how long does the car move uniformly?
1 Answer
Explanation:
Let the car cover three distances under accelerating, uniform and decelerating conditions
Using the kinematic equations
Accelerating
Let
From (2) and (4)
Uniform motion
Using (3) and (4)
Decelerating
Using (1) and (4)
Using (2) and (4)
We know that
Average Velocity
Inserting given values in SI units we get
Using (5) (6) and (8) we get
Given is total time
Using (7)
Inserting this value is (9) we get
Roots of this quadratic are found by split the middle term and we get
Inserting these values one by one in (10) and ignoring other root which gives negative time