A body of mass m moving along a straight line covers half the distance with a speed of . The remaining half of the distance is covered in two equal time intervals with a speed of and respectively. The average speed of the particle for the entire journey is
Step 1: Given data
Step 2: Average speed
The average speed of a body is,
Step 3: Calculation of
Let be the time taken by the body in the first half and be the time taken by the body in each equal interval in the second half. And s be the total distance travelled by the body.
We know, .
Now for the first half, the time is taken by the body,
(where Is the distance travelled by the body in the first half )
Step 4: Calculation of
In the second half,
Step 5: Calculation of total time.
Now, the total time is taken by the body in the complete journey is,
Step 6: Calculation of average speed
Again,
Therefore, the average speed of the body is . So option (B) is correct.