The body B is moving with velocity v2 and acceleration a2 in a straight line. The body A at a distance ‘d’ from B moving with velocity v1 and acceleration a1 along the same line, will catch up the body B, if-

1. v1>v2
2. a1>a2
3. a1>a2 and v1>v2.
4. data unsufficient.

Answer is B. how?

To determine whether body A will catch up to body B, we need to analyze the conditions given in the question. Let's break down the information step by step.

Understanding the Motion of Both Bodies

Body A is moving with a velocity of v1 and an acceleration of a1, while body B is moving with a velocity of v2 and an acceleration of a2. Both bodies are moving in the same direction along a straight line, with body A initially at a distance 'd' behind body B.

Key Conditions for Catching Up

For body A to catch up to body B, it must overcome the initial distance 'd' between them. This can happen under certain conditions:

• Relative Velocity: Body A must be moving faster than body B, which means v1 must be greater than v2 (v1 > v2).
• Acceleration Comparison: Body A should also have a greater acceleration than body B (a1 > a2). This ensures that not only is body A faster initially, but it also gains speed more quickly over time.

Analyzing the Given Conditions

The conditions provided in the question are:

• v1 > v2
• a1 > a2

Since both conditions are satisfied, we can conclude that body A will indeed catch up to body B. Let’s delve deeper into why this is the case.

Mathematical Representation

We can represent the positions of both bodies as functions of time:

• Position of body A: xA(t) = xA0 + v1*t + 0.5*a1*t²
• Position of body B: xB(t) = xB0 + v2*t + 0.5*a2*t²

Here, xA0 is the initial position of body A, and xB0 is the initial position of body B. Since body A starts at a distance 'd' behind body B, we can express this as:

• xB0 = xA0 + d

Setting Up the Equation

To find when body A catches up to body B, we set their positions equal:

Substituting the position equations, we get:

By simplifying this equation, we can isolate terms involving time (t) and analyze the conditions under which body A will catch up to body B.

Conclusion on the Conditions

Given that v1 > v2 and a1 > a2, body A not only starts faster but also accelerates faster than body B. This means that over time, the gap 'd' will decrease, and eventually, body A will reach body B. Therefore, the answer to the question is indeed that body A will catch up to body B under the conditions provided.