A body starts with a certain initial velocity and moves with...

A body starts with a certain initial velocity and moves with a constant deceleration along a straight line. If the distances travelled in the 5 th and 7 th second are in the ratio $\frac{31}{27}$, the body will come to a stop in time (a) $40 \mathrm{~s}$ (b) $30 \mathrm{~s}$ (c) $20 \mathrm{~s}$ (d) $10 \mathrm{~s}$

A body starts with a certain initial velocity and moves with a constant deceleration along a straight line. If the distances travelled in the 5 th and 7 th second are in the ratio $\frac{31}{27}$, the body will come to a stop in time
(a) $40 \mathrm{~s}$
(b) $30 \mathrm{~s}$
(c) $20 \mathrm{~s}$
(d) $10 \mathrm{~s}$

Key Concepts

Uniformly Accelerated Motion

This concept refers to motion in which an object experiences a constant acceleration (or deceleration). The basic kinematic equations of motion apply in this scenario, establishing relationships between initial velocity, acceleration, time, and displacement. Such equations are essential for solving problems involving objects that either speed up or slow down at a uniform rate.

Distance Traveled in the nth Second

This concept involves calculating the distance an object travels specifically during the nth second of its motion. The formula for the displacement in the nth second provides a way to analyze segments of motion by comparing the distances covered in different time intervals. It is crucial for setting up ratio relationships when given distances in specific seconds.

Deceleration

Deceleration is a form of uniform acceleration where the magnitude of acceleration acts opposite to the direction of motion, causing the velocity to decrease over time. Understanding deceleration is key when applying the kinematic equations to determine parameters such as the time taken for a moving object to come to a complete stop.

Time to Stop Calculation

This concept involves using the kinematic relationships to find when an object's velocity becomes zero. By setting the final velocity to zero and applying the equations of motion with the known initial velocity and deceleration, one can determine the total time required for the object to stop. This method is critical when solving problems requiring the computation of stopping time.

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