A body, which can move with constant acceleration of 2 m s^-2 and constant deceleration of 4

step 1 Hello students. So for this question we can draw the velocity time graph and this will be obtain

A body, which can move with constant acceleration of 2 m...

A body, which can move with constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ and constant deceleration of $4 \mathrm{~m} \mathrm{~s}^{-2}$ starts from rest at A along a straight line and stops at B and covers that total distance with maximum average velocity possible. If the distance moved during deceleration is $2 \mathrm{~m}$, then (a) maximum velocity $=4 \mathrm{~m} \mathrm{~s}^{-1}$ (b) average velocity $=2 \mathrm{~m} \mathrm{~s}^{-1}$ (c) total distance $\mathrm{AB}=6 \mathrm{~m}$ (d) total time of travel $=4 \mathrm{~s}$

A body, which can move with constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ and constant deceleration of $4 \mathrm{~m} \mathrm{~s}^{-2}$ starts from rest at A along a straight line and stops at B and covers that total distance with maximum average velocity possible. If the distance moved during deceleration is $2 \mathrm{~m}$, then
(a) maximum velocity $=4 \mathrm{~m} \mathrm{~s}^{-1}$
(b) average velocity $=2 \mathrm{~m} \mathrm{~s}^{-1}$
(c) total distance $\mathrm{AB}=6 \mathrm{~m}$
(d) total time of travel $=4 \mathrm{~s}$

Key Concepts

Optimization of Average Velocity

Maximizing or optimizing the average velocity in a motion problem under given constraints requires minimizing the overall travel time while maintaining continuity in the motion. This often involves ensuring that the maximum possible instantaneous velocity is utilized during the transition between acceleration and deceleration phases. Understanding how the rates of acceleration and deceleration influence the time and distance in each segment is essential for achieving an optimal solution.

Interdependence of Acceleration and Deceleration Phases

The final velocity reached at the end of the acceleration stage is typically the initial velocity for the deceleration stage. The constraints in one phase (for instance, the distance needed for deceleration) directly affect the conditions in the other phase (such as the maximum achievable velocity). Recognizing this interdependence is key to solving for variables like maximum velocity or total distance.

Phase-wise Motion Analysis

In many motion problems, the overall movement is divided into different stages, such as acceleration and deceleration phases. Analyzing each phase separately using appropriate kinematic formulas is vital, as the conditions (like acceleration rate or distance covered) may differ across segments. This approach helps in piecing together the overall motion by ensuring consistency at the transition points between the phases.

Kinematics Under Constant Acceleration

This concept involves applying the standard equations of motion for bodies undergoing uniform acceleration. These equations, such as v = u + at and v² = u² + 2as, allow one to calculate the velocity, displacement, and time of travel during intervals of acceleration or deceleration. Understanding these relationships is crucial in solving problems that involve changes in motion over time.

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