Question

Two particles A and B start from rest and move for equal time on a straight line. The particle A has an acceleration a for the first half of the total time and 2a for the second half. The particle B has an acceleration 2a for the first and a for the second half. Which particle has covered larger distance?

Answer 1

Let '2t' be the total time for which the particles move, v_A and v_B the velocities of particle A and B after first half of the total time. From the equation v=u+at, 

For particle A, u=0, vA = at  

using equation s=ut+1/2 at² 

Total distance traveled by particle A 

=(ut+½at²)+(vAt+½2at²)  

=(0+½at²)+(at.t+at²) 

=½at²+2at²  

=2.5 at²  For particle B, v_B

=0+2at =2at,  

So total distance traveled by particle 

B =(ut+½2at²)+(vBt+½at²)    

=(0+at²)+(2at.t+½at²)  

=at²+2at²+½at² =3at²+½at²  

=3.5 at²