To get the initial velocity and acceleration of the particle... well, we can't. There isn't enough information. I am going to assume that the motion is "smooth:" the final velocity of the initial phase is the same as the constant velocity of the second phase.1. A particle moves for 4 seconds in a straight line with uniform acceleration and describes 52 m. It then travels with uniform speed covering 48 m in 3 s. It is brought to rest by a retardation twice that of the initial acceleration.
So assuming an origin at the point where the particle was when the time started and a +x direction in the direction of the initial acceleration we have:
Solving the top equation for v_0 I get:
Inserting this into the second equation gives:
Solving the quadratic for a I get that:
We discard the negative solution since the acceleration is defined to be positive in the first phase, so .
The final retardation (acceleration) is just twice the negative of the acceleration in the first part so .
You can use to find the distance travelled in the last phase of the motion. I leave that to you.