## Sunday, October 9, 2016

### Motion in One Dimension Problems with Solutions One

In one dimensional motion, we study about the motion of a body along one dimension let it be X- axis or Y- axis. Here in this topic we are restricting our self to study about the way how the body is moving and we are not studying why the body is moving. That means we are not yet bothered about the cause of the motion. To study the motion of the body in one dimension, we have four equations of motion which links physical quantities like initial velocity, final velocity, acceleration, displacement and time.

Problem One

In the problem it is given that the body covers a certain distance in a given time and in the next specified time, it covers some more distance. We are interested in measuring the velocity of the body.

Solution

We know that the second equation of motion relates the displacement of the body with time, initial velocity and acceleration. By substituting the given data in that equation, we can  get an equation between initial velocity and acceleration as shown in the diagram below.

Further by substituting the given values of the second case in the same equation of motion, we can get one more equation with initial velocity and acceleration. By  solving the two equations, we can find initial velocity and acceleration. By using this values in the final velocity equation in terms of initial velocity, acceleration and time, we can find the velocity of the given body after specified time as shown in the diagram below.

Problem Two

It is given in the problem that a body first accelerates for a specified time and then retards for some more time. We need to find the relation between them with the time.

Solution

It is given in the problem that the body starts from rest so that it has zero initial velocity. We can find the maximum velocity acquired by the body after a specified time. The body further starts retarding and it means its velocity is further going to decrease and it finally comes to the state of rest.

By substituting the data in the same equation, we can get one more relation and by simplifying them further, we can solve the problem as shown in the diagram below.

Problem Three

It is given in the problem that there are two  trains travelling in the opposite directions  and their lengths were given to us. We need to know how  much time  does it takes for these trains to cross each other ?

Solution

Let there is a certain time in  which these two trains were crossing each other. Let the first train covers a distance in that given time and the second train covers the remaining the distance in that specified time. We can use second equation of motion with the give n data and simplify the equations as shown in the diagram below.

Problem Four

In this problem a rod of known length is placed to the incline of the wall with a known angle. If we know the speed of the lower part of the rod, we need to know the speed of the other end in the vertical direction ?

Solution

Let us assume that the rod one end is at a distance X and other end is at a distance Y from the horizontal and vertical direction. Basing on the basic rule of trigonometry, we can find the relation of them with the length.

These are the displacements and we are interested with speeds. We know that the rate of change of displacement is the velocity and hence we shall differentiate the equation.

As the length of the rod is constant, its differentiation with time is zero. Taking that into consideration, we can solve the problem as shown in the diagram below.

### Units and Dimensions Problems and Solutions Five

Units and Dimensions Problems and Solutions Six