# 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