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

A body starts with a certain initial velocity and moves with constant deceleration along a straight line. If distances travelled in the 5 th and 7 th second are in the ratio $\frac{31}{27}$, the distance travelled by the body before it stops is (a) $50 \mathrm{~m}$ (b) $100 \mathrm{~m}$ (c) $150 \mathrm{~m}$ (d) data insufficient

A body starts with a certain initial velocity and moves with constant deceleration along a straight line. If distances travelled in the 5 th and 7 th second are in the ratio $\frac{31}{27}$, the distance travelled by the body before it stops is
(a) $50 \mathrm{~m}$
(b) $100 \mathrm{~m}$
(c) $150 \mathrm{~m}$
(d) data insufficient

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Key Concepts

Uniformly Accelerated Motion

This concept refers to motions where the acceleration remains constant over time. Under such conditions, the basic equations of motion apply, allowing relationships to be established between displacement, initial velocity, time, and acceleration. This framework is fundamental in kinematics and is used to analyze both accelerating and decelerating bodies.

Distance Traveled in the nth Second

In uniformly accelerated motion, the distance covered during any specific second can be expressed using a formula derived from the kinematic equations. This expression takes into account the initial velocity and the constant acceleration, characterizing the displacement during an interval that is exactly one second. This concept is useful for understanding how motion is distributed over successive seconds.

Stopping Distance Calculation

Stopping distance is the total distance a moving object travels from the beginning of deceleration until it comes to rest. It is computed using kinematic equations that relate the initial velocity, constant deceleration, and displacement. This calculation is essential for assessing safety and designing systems where controlled deceleration is critical.

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