Question

What is the nature of the distance time graphs for uniform and non-uniform motion of an object moving in a straight line?
(a). Uniform: Straight line; Non uniform: Straight line
(b). Uniform: Straight line; Non uniform: Curved
(c). Uniform: Curved; Non uniform: Straight line
(d). Uniform: Curved; Non uniform: Curved

Answer 1

Hint: To solve this question we will be using the basic concepts of uniform and non-uniform motion i.e. slope of displacement-time gives velocity of an object and slope of velocity and acceleration gives us acceleration of the object. Using this we will solve the problem and find the answer.

Complete step by step answer:
Now, in question we are asked to find the nature of distance – time graphs for uniform and non-uniform motion, so, first of all we will use the distance time graph for uniform motion.
Now, if an object is in uniform motion, then it means that its acceleration with respect to time is zero which means the velocity of the object is constant. It can be expressed mathematically as,
$v=\text{constant}$……………..(i)
$a=0$ ………………………..(ii)
Now, we know that velocity means slope of displacement and time, which can be expressed mathematically as,
$v=\dfrac{dx}{dt}$
Now, substituting the values of expression (i) in the equation above we will get,
$v=\dfrac{dx}{dt}=\text{constant}$
$\Rightarrow dx=kdt$
Where, k is any constant, dx is displacement and dt is time.
So, from the above expression it can be said that the value of displacement will be equal to the value to value of time. So, the graph will be a straight line and it can be shown as,

Now, for non-uniform motion of an object we know that velocity will not be constant as the acceleration will not be zero, so this can be shown mathematically as,
$v\ne \text{constant}$……………..(iii)
$a\ne 0$ ………………………..(iv)
So, the slope of displacement and time graph will not be constant which can be given as,
$v=\dfrac{dx}{dt}\ne \text{constant}$
So, from this we can see that the value of velocity changes with changes in displacement and time so the graph will not be straight line and it can be any curve depending on the values of displacement and time.

Hence the correct answer is option (b).

Note: Students can also solve this sum by putting different values in the equation of velocity and then plot the graph and find the answer but it is a very tedious method and less preferable also. Students must know the difference between uniform and non-uniform motion because they might make mistakes in considering them as constant or zero.