We would like to solve a problem basing on relative velocity concept. There are two particles separated from a origin and the two positions are perpendicular to each other. They are moving with a known velocity. We need to know the nearest distance between them. The problem is as shown in the diagram below.

**Solution**

Let us consider that A and B are the two bodies in the given problem and they are located perpendicular to the origin. Let A has travelled for one second and hence it covers three meter in that time. As it is given that it is initially at ten meter from the origin, after one second it is at the distance of seven meter.

Simultaneously the body B has moved a distance four meter from the origin. So we can find the shortest distance between the two bodies as shown in the diagram below.

**Problem**

In this one dimensional motion problem, the position of the body is given in terms of time and constants as shown in the diagram below.We need to know the particular value of the time at which acceleration of the body is zero.

**Solution**

It is given that displacement in terms of time.By differentiating displacement once with respect to time we can velocity and by differentiating velocity with respect to time we get acceleration.We shall equate acceleration to zero as per given problem to get the time required in the problem.

By using the basic rule of differentiation, we can solve the problem as shown in the diagram below.

**Problem**

This problem is also a similar problem to the above. We need to know what is the displacement of the particle at the instant when the velocity of the body is zero.

**Solution**

The given equation is in terms of displacement and by rearranging them we can get the displacement equation in terms of time as shown in the diagram below.

By differentiating the displacement once with respect to time we get velocity. As per the condition given in the problem, we need to equate it to zero. Thus it is found that velocity of the body becomes zero after three seconds. By substituting that value in the displacement equation, we can get the displacement as shown in the diagram below.

**Problem**

This problem is also about the relation between displacement and time with some constants involved. The problem is as shown in the diagram below. We need to find the displacement after a certain time to verify the first option.

We need to check the velocity to verify the second option. The third option is regarding the new new displacement of the particle.

**Solution**

By differentiating the displacement once with respect to time as shown in the diagram below, we can get the velocity of the particle. By differentiating once again, we can get acceleration of the same particle. By substituting the given condition of the time, we can solve the problem as shown in the diagram below.

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