Question

With what speed should a car travel so that it can cover a distance of $$5km$$ in $$5sec$$?
A) $$1km/h$$
B) $$5km/h$$
C) $$12km/h$$
D) $$60km/h$$

Answer 1

Hint: When a body moves some distance in a few time intervals then the rate of change of distance with respect to time is called speed. In this given question we have to convert both physical quantities in the MKS system and then we can solve this question by applying distance time relation.

Formula used: when a body covers distance of several kilometre $\mathrm{\Delta }s$ in some time interval $\mathrm{\Delta }t$ then the speed of body $v$ is given by
$v={\displaystyle \frac{\mathrm{\Delta }s}{\mathrm{\Delta }t}}$

Complete step by step solution: For finding the speed of a moving body we should know about distance travelled by the body and the time interval in which the body covered the distance. In this question, we have the speed in kilometres and time is in minutes. So, firstly we have to convert them into an MKS system. By the question the distance covered by the body $\mathrm{\Delta }s=5km$ and time is given $\mathrm{\Delta }t=5min$
Now,
$$\begin{gathered} \mathrm{\Delta }s=5km \\ \Rightarrow \mathrm{\Delta }s=5\times 1000m \\ \therefore \mathrm{\Delta }s=5000m \end{gathered}$$
And
$$\begin{gathered} \mathrm{\Delta }t=5min \\ \Rightarrow \mathrm{\Delta }t=5\times 60\sec \\ \therefore \mathrm{\Delta }t=300\sec \end{gathered}$$
So, if the speed of the body is given as rate of change of distance.
$v={\displaystyle \frac{\mathrm{\Delta }s}{\mathrm{\Delta }t}}$
Substituting the values in the above equation, we have-
$$\begin{gathered} \Rightarrow v={\displaystyle \frac{5000}{300}}m/\sec \\ \therefore v=16.67m/\sec \end{gathered}$$
Now, converting meters in kilometres and seconds in hours, we have-
$$\begin{gathered} \Rightarrow v=16.67\times {\displaystyle \frac{3600}{1000}}km/h \\ \Rightarrow v={\displaystyle \frac{60012}{1000}}km/h \\ \therefore v=60km/h \end{gathered}$$
Where $1m={\displaystyle \frac{1}{1000}}km$ and $1\sec ={\displaystyle \frac{1}{3600}}h$
Hence, the body should move with a velocity $$60km/h$$ so that the body can cover $$5km$$ in $$5min$$.

Therefore, option (A) is correct.

Note: The unit of speed is meter per second in MKS system. It is necessary to convert given physical quantities into MKS systems. We can also find the speed in the CGS system of measurements by converting distance in centimetres and time interval in seconds. We can also find the speed of two moving bodies by comparing their distance covered with respect to time if both bodies cover equal distance in equal time then both the bodies are said to be in same speed. If one of those bodies is the same distance in less time with respect to another body then that body has greater speed than the other body.