Question

A car travels \[200km\] in $2hours$ and travels \[240km\] in the next $3hours$ . If the acceleration is constant then the distance it will travel in the next one hour is:
A. $\left( a \right){\text{ 64km}}$
B. $\left( b \right){\text{ 72km}}$
C. $\left( c \right){\text{ 84km}}$
D. $\left( d \right){\text{ 40km}}$

Answer 1

Hint: Here, for solving this question we will use the concept of slope. As we know that the slope is used for the inclination of line or steepness of it. So, it is given by \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]. So by substituting the values, we will get the solution.

Formula used:
The slope of a line is given by,
\[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
Here,
$m$ , will be the slope of a line
$\left( {{x_1},{y_1}} \right)$ , will be the coordinates of the first point in the line and
$\left( {{x_2},{y_2}} \right)$ , will be the coordinates of the second point in the line.

Complete step-by-step answer:
Since in the question it is given that we have the distance traveled by car in $2hours$ is \[200km\] and the distance traveled by car in the next $3hours$ is \[240km\] . So we have to find the distance it travels in the next one hour.
Since the acceleration will be constant. Therefore, the distance it will travel in the next one hour will be shown by the slope and the coordinates will be $\left( {2,200} \right)$ and $\left( {3,240} \right)$ .
So by using the slope formula which is given by
\[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
On substituting the values, in the above slope equation, we get
\[ \Rightarrow m = \dfrac{{240 - 200}}{{3 - 2}}\]
On solving the numerator and denominator, we get
\[ \Rightarrow m = \dfrac{{40}}{1}\]
And therefore the slope will be $40$ .

Hence, the distance traveled by car in the next one hour is $40km$.

Note: In this type of question, we just need the formula and we can easily solve it by substituting it. So if a line is increasing and goes up from left to right then the slope will be positive and similarly, the opposite of it will be negative. And if it is horizontal then it will be zero.