Two cars A and B are moving towards each other on a straight...

Two cars $A$ and $B$ are moving towards each other on a straight road with velocity $10 \mathrm{~m} / \mathrm{sec}$. and $12 \mathrm{~m} / \mathrm{sec}$. respectively. When they are $160 \mathrm{~m}$ apart, then each car decelerates at $2 \mathrm{~m} / \mathrm{sec}^{2}$ until they stop in order to avoid collision. Calculate the distance between them when they come to rest.

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Key Concepts

Uniform Deceleration

Uniform deceleration refers to the process of slowing down at a constant rate. In many real-world scenarios and physics problems, such as vehicles coming to a stop, the deceleration is constant, allowing the use of specific kinematic equations to predict distances and times accurately.

Kinematic Equations

Kinematic equations describe the relationships between displacement, velocity, acceleration, and time for objects moving with constant acceleration. These equations are fundamental in solving problems in one-dimensional motion, including calculating stopping distances when deceleration is applied.

Stopping Distance

Stopping distance is the measure of the distance an object travels while decelerating to a complete stop. It is typically calculated using the formula derived from kinematic equations, v²/(2a), where v is the initial velocity and a is the magnitude of the deceleration.

Relative Motion

Relative motion considers the movement of two or more objects with respect to each other. In problems involving multiple moving objects, such as two cars approaching one another, understanding relative motion is crucial for determining the separation distance at various points in time, especially when factors like deceleration are involved.

Transcript

00:01 Hello everyone, let us do the following question.

00:03 The question is two cars a and b are moving towards each other on a straight line with the velocity of 10 meter per second.

00:11 Velocity of a car is 10 meter per second and velocity of b car is 12 meter per second when they are 160 meter apart.

00:23 When the distance between them is a 160 meter.

00:26 Then each car d accelerates at 2 meter per second until in order to avoid collision calculate the distance between them when they comes to rest.

00:36 We have to calculate the distance when they both will come to rest.

00:40 We will consider here two cars.

00:43 We will consider here two cars.

00:45 Here is car a and here is car b.

00:48 Here is car first and here is car second.

00:52 Car a is moving with 10 per second.

00:55 We'll also.

00:55 Of a is 10 meter per second and velocity of car b is a velocity of car b is 12 meter per second velocity of car b is a 12 meter per second distance between both the cars is 160 meter we have to find distance when they both will come to rest now we'll solve one by one firstly we will solve this four car one we'll solve this 4car 1.

01:26 We have equation v is equal to u plus at.

01:31 V is equal to 0.

01:34 Value of u is 10, acceleration is minus 2 as they are retarding...

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