Question

The odometer of a car reads \[57321.00km\] when the clock shows the time $8:30\text{AM}$. What is the distance moved by the car, if at $8:50\text{AM}$, the odometer reading has changed to $57336.00km$? Calculate the speed of the car in $\dfrac{\text{km}}{\text{min}}$ during this time. Express the speed in $\dfrac{\text{km}}{\text{hour}}$ also.

Answer 1

Hint: The odometer is a device used to calculate the distance travelled by a vehicle. It is fitted right next to the speedometer. To get the distance travelled by the car in between the given time calculate the difference in readings of the odometer. To get the speed divide the distance travelled by the car by the total time difference.

Formulas used:
$\text{speed=}\dfrac{\text{distance}}{\text{time}}$

Complete step by step answer:
At $8:30\text{AM}$ the odometer reading was \[57321.00km\].
At $8:50\text{AM}$the odometer reading is $57336.00km$.
Total time difference is $\Delta t=8.50-8.30=20\min $
Total distance travelled during this time is $\Delta S=57336.00-57321.00=15km$
Speed of any object is defined as the ratio of distance travelled by the time interval, i.e.
$v=\dfrac{\Delta S}{\Delta t}$
So the speed of the vehicle in $\dfrac{\text{km}}{\text{min}}$is
$v=\dfrac{15km}{20\min }=0.75\dfrac{\text{km}}{\text{min}}$
So the car has velocity of $0.75\dfrac{\text{km}}{\text{min}}$.
To calculate the speed of the car in $\dfrac{\text{km}}{\text{hour}}$ we have to convert minutes to hours.
We know
 $\begin{align}
  & 60\min =1\text{hour} \\
 & \Rightarrow 1\min =\dfrac{1}{60}\text{hour} \\
 & \Rightarrow \text{20min=}\dfrac{1}{60}\times \text{20hour=}\dfrac{1}{3}\text{hour} \\
\end{align}$
So now the time interval is $\dfrac{1}{3}\text{hour}$. i.e. the car covers $15km$ in $\dfrac{1}{3}\text{hour}$. So the speed of the car is
$v=\dfrac{15km}{\left( \dfrac{1}{3} \right)\text{hour}}=45\dfrac{\text{km}}{\text{hour}}$
So the speed of the car in $0.75\dfrac{\text{km}}{\text{min}}\text{ or }45\dfrac{\text{km}}{\text{hour}}$

Additional Information:
The odometer measures the distance travelled by the vehicle. But the speedometer calculates the instantaneous speed of the vehicle.

Note:
A body is said to be moving if it changes its position by the passage of time. If a body moves it will have some displacement. The displacement of a body is defined as the difference between its final position and initial position. The displacement doesn’t depend upon the path followed. So if you move some distance in a circular path your displacement will be zero because your position isn’t changed but the distance travelled is zero. So the displacement of an object is a vector quantity and only depends upon the initial position and final position.