Answer:



negative sign denotes deceleration.


Step-by-step explanation:
Given:
- initial speed of blue car,

- initial speed of yellow car,

- acceleration rate of blue car,

- time for which the blue car accelerates,

- time for which the blue car moves with uniform speed before decelerating,

- total distance covered by the blue car before coming to rest,

- distance at which the the yellow car intercepts the blue car just as the blue car come to rest,

1)
Speed of blue car after 2.6 seconds of starting the motion:
Applying the equation of motion:



Speed of blue car after 7.2 seconds of starting the motion:
∵The car accelerates uniformly for 3.3 seconds after which its speed becomes uniform for the next 14.3 second before it applies the brake.
so,



Distance travelled by the blue car before application of brakes:
This distance will be
(distance travelled during the accelerated motion) + (distance travelled at uniform motion)
Now the distance travelled during the accelerated motion:



Now the distance travelled at uniform motion:


Finally:



Acceleration of the blue car once the brakes are applied
Here we have:
initial velocity,

final velocity,

distance covered while deceleration,


Using the equation of motion:


negative sign denotes deceleration.
The total time for which the blue car moves:
........................(1)
Now the time taken to stop the blue car after application of brakes:
Using the eq. of motion:



Putting respective values in eq. (1)


For the acceleration of the yellow car:
We apply the law of motion:

Here the time taken by the yellow car is same for the same distance as it intercepts just before the stopping of blue car.
Now,

