Question

A car covers $30km$ at a uniform speed of $60{\text{ }}km/hr$ and the next $30km$ at the uniform speed of $40{\text{ }}km/hr$. The total time taken is?
$(A)\;30min$
$(B)\;\;45min$
$(C)\;\;75min$
$(D)\;\;120min$

Answer 1

The definition of the uniform speed has to be known. By using the given distances and speeds in this formula the times can be calculated. Note that, speed is the ratio of distance and time. But, if the speed is non-uniform, the average speed is taken under-count. The above-mentioned formula has to be used for the two parts of the journey and then the times that are found are to be added for calculating the total time taken in the whole journey.

Formula Used:
The relation between the uniform Speed of the object $(v)$, distance traveled by the object$(s)$, and the Time taken by the object to cover the distance $(t)$,
$v = \dfrac{s}{t}$

Complete step-by-step solution:
Case -1
When the car is moving with the speed of $60{\text{ }}km/hr$ and covers a distance of $30km$.
So, during this period
From the relation, $v = \dfrac{s}{t}$
by putting, $v = 60km{\text{ }}/hr$ and, $s = 30km$
$\Rightarrow 60 = \dfrac{{30}}{t}$
$\Rightarrow t = \dfrac{{30}}{{60}}hr$
$\Rightarrow t = \dfrac{1}{2}hr = 30\min$
Case -2
When the car is moving with the speed of $40{\text{ }}km/hr$ covers a distance of $30km$.
So, during this period
From the relation, $v = \dfrac{s}{t}$
by putting, $v = 40km{\text{ }}/hr$ and, $s = 30km$
$\Rightarrow 40 = \dfrac{{30}}{t}$
$\Rightarrow t = \dfrac{{30}}{{40}}hr$
$\Rightarrow t = \dfrac{3}{4}hr = 45\min$
Total time is taken to complete the journey $= 30 + 45 = 75\min$
So Option (C) is the correct answer.

Note: Uniform motion- A type of motion of an object in which the object travels in a straight line and its velocity remains constant along that line. During the uniform motion the object covers equal distance in an equal interval of time the acceleration of the body will be equal to zero as the rate of the change in velocity is zero.
Non-Uniform Motion- When an object moves with a changeable speed at certain times and it does not cover the same distance in equal time intervals, irrespective of the time interval duration - This type of motion is defined as the non-uniform motion. In this type of motion acceleration of the body is not zero.

ComparisonParameters	Uniform Motion	Non- Uniform Motion
initial Speed		The motion is different from the initial speed of the object.
Acceleration	It has zero acceleration.	It has non-zero acceleration.
Distance	Covers the same distances in an equal time interval.	Covers different distances in equal time intervals.
Graph	The Distance-time graph shows a straight line.	The Distance-time graph shows a curved line.