Question

On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a point. Abhijit moves with a constant speed. Vani starts with a constant acceleration from rest. They meet again on the track with the same speed. Which of the following is correct?

• A. Abhijit travelled double the distance travelled by Vani.
• B. Abhijit travelled half the distance travelled by Vani.
• C. Abhijit travelled the same distance travelled by Vani.
• D. Abhijit travelled 4/3 of the distance travelled by Vani.

Hint:

For any motion starting from rest with constant acceleration, the average velocity is exactly half of the final velocity.
Since Abhijit travels at a constant velocity equal to Vani's final velocity, Abhijit's average speed is twice that of Vani's.
Consequently, for the same time interval, Abhijit must travel twice the distance.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question involves analyzing the kinematics of two bodies moving along a circular path in opposite directions.
Abhijit moves with a constant speed, whereas Vani starts from rest and moves with a constant acceleration.
We need to determine the relation between the distances traveled by both cyclists when they meet again with the same speed.

Step 2: Key Formula or Approach:
For Abhijit, who moves with a constant speed \(v_A\).:
The distance traveled in time \(t\) is:
\[ d_A = v_A \cdot t \]
For Vani, who starts from rest (\(u_V = 0\)) with constant acceleration \(a_V\).:
Her speed at time \(t\) is:
\[ v_V = a_V \cdot t \]
The distance traveled by her in time \(t\) is:
\[ d_V = \frac{1}{2} a_V \cdot t^2 \]

Step 3: Detailed Explanation:

• Let the time at which they meet again on the track be \(t\).

• According to the problem statement, at this meeting time \(t\), their speeds are equal.

• Therefore, we can equate their speeds:
\[ v_A = v_V(t) \implies v_A = a_V \cdot t \]

• Now, let us express the distance traveled by Abhijit using this speed relation:
\[ d_A = v_A \cdot t = (a_V \cdot t) \cdot t = a_V \cdot t^2 \]

• Next, we calculate the distance traveled by Vani in the same time interval:
\[ d_V = \frac{1}{2} a_V \cdot t^2 \]

• Comparing the two distances, we find:
\[ d_A = 2 \cdot d_V \]

• This implies that the distance traveled by Abhijit is twice the distance traveled by Vani.

Step 4: Final Answer:
Thus, Abhijit travelled double the distance travelled by Vani.