A body travelling along a straight line traversed one third of the total distance with a velocity 4m s⁻¹. The remaining part of the distance was covered with a speed 2m s⁻¹ for half of time then remaining part is covered with 6m/s. The mean velocity averaged over the whole time of motion is
Physics · Mixed Chapter
JEE Mains

Question

A body travelling along a straight line traversed one third of the total distance with a velocity 4m s⁻¹. The remaining part of the distance was covered with a speed 2m s⁻¹ for half of time then remaining part is covered with 6m/s. The mean velocity averaged over the whole time of motion is

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Let total distance be 3d. First d is travelled at 4 m/s, requiring time t₁=d/4. Step 2: Remaining 2d is travelled for equal time intervals at speeds 2 and 6 m/s. Since distances in these equal intervals add, their mean speed is (2+6)/2=4 m/s. Hence t₂=(2d)/4=d/2. Step 3: Total time =d/4+d/2=3d/4; total distance =3d. Step 4: Mean speed (and mean velocity along the straight uninterrupted direction) =3d/(3d/4)=4 m/s. Answer: 4.