 Hi and welcome to our session. Let us discuss the following question. The question says, a particle starting from some initial velocity and moving with uniform acceleration acquires a velocity of 20 centimeter per second after moving through 10 centimeter from a point P to Q and a velocity of 30 centimeter per second after further moving 20 centimeter from Q to R in the same direction. Find first part is its velocity at the point P. Second part is its acceleration. Third part is the time it will take and the distance it will move from R to attain a velocity of 40 centimeter per second. Begin with the solution. Now the initial position of the particle is at the point P. According to the question, particle moves through 10 centimeter from point P to Q and it acquires a velocity of 20 centimeter per second. After that, it moves from point Q to R and both of these points are at 20 centimeters far from each other and the velocity of the particle is 30 centimeter per second. We have to find the velocity of the particle at point P then we have to find its acceleration then we have to find the time it will take and the distance it will move from R to attain a velocity of 40 centimeter per second. Now let's first consider distance Q R. This velocity becomes the initial velocity of the particle when it's moved from point Q to R. So we have U as 20 centimeter per second and this is the final velocity of the particle that is 30 centimeter per second. Distance moved by the particle from point Q to R is 20 centimeters. Now we know that V squared is equal to U squared plus 2 AS So by using this equation, we will now find A. Now by substituting values of U, V and S, we get 30 squared equals to 20 squared plus 2 into A into 20. Now this implies 900 is equal to 400 plus 40 A. This implies 500 is equal to 40 A and this implies 25 by 2 centimeter per second squared. So acceleration of the particle is 25 by 2 centimeter per second squared. Distance PQ let initial velocity of particle is U centimeter per second. The velocity of the particle when it travels from point P to Q is 20 centimeter per second and the distance between point P and point Q is 10 centimeters. So S is equal to 10 centimeters. Acceleration of the particle is 25 by 2 centimeter per second squared. Now we know that V squared is equal to 2 squared plus 2 AS. So by using this equation, we will now find initial velocity of the particle. Now V is 20 centimeter per second. U is initial velocity of particle. A is 25 by 2 centimeter per second squared and S is 10. This implies 400 is equal to U squared plus 250. This implies U squared is equal to 150. This implies U is equal to square root of 150 meter per second. This implies U is equal to 5 into 6 centimeter per second. Now for motion after R, velocity of the particle is 40 centimeter per second. Acceleration of the particle is 25 by 2 centimeter per second squared. And initial velocity of the particle is 30 centimeter per second. We know that V is equal to U plus 80. So now by using this equation, we will now find T. V is 40, U is 30, and A is 25 by 2. This implies 10 is equal to 25 by 2 into T. And this implies 20 by 25 is equal to T. That means T is equal to 20 by 25 seconds. Now we also know that V squared is equal to U squared plus 2A S. By using this equation, we will now find S. This implies S is equal to V squared minus U squared divided by 2A. This is equal to V minus U into V plus U divided by 2A 40. And U is 30, 55 by 2. This is equal to 10 into 70 divided by 25. This is equal to 28 centimeters. A required answer of the first 5 into root 6 centimeter per second, the second part per second squared. So this is the situation by taking care.