Question

Arun completed a 100 m race in 16 s., while Karthik finished it in 13 s. Who ran faster?

Answer 1

Hint: Use the relation between velocity, displacement and time to relate the velocities of Arun and Karthik. Whoever ran faster has the greater velocity.

Formula used:
\[v = \dfrac{d}{t}\]
Here, v is the velocity, d is the displacement and t is the time taken.

Complete step by step answer:
We have the relation between velocity, displacement, and time as below,
\[{\text{Velocity}} = \dfrac{{{\text{Displacement}}}}{{{\text{Elapsed}}\,\,{\text{time}}}}\]
whoever ran faster has greater velocity. Therefore, we calculate the velocity of both Arun and Karthik as follows,
\[{v_{Arun}} = \dfrac{d}{{{t_{Arun}}}}\] …… (1)
Here, \[{t_{Arun}}\] is the time taken by Arun to finish the race.
Substitute 100 m for d and 16 s for \[{t_{Arun}}\] in the above equation.
\[{v_{Arun}} = \dfrac{{100\,m}}{{16\,s}}\]
\[ \Rightarrow {v_{Arun}} = 6.25\,m/s\]
Now, we can calculate the velocity of Karthik as same as above,
\[{v_{Karthik}} = \dfrac{d}{{{t_{Karthik}}}}\] …… (2)
Here, \[{t_{Karthik}}\] is the time taken by Karthik to finish the race.
Substitute 100 m for d and 13 s for \[{t_{Karthik}}\] in the above equation.
\[{v_{Karthik}} = \dfrac{{100\,m}}{{13\,s}}\]
\[ \Rightarrow {v_{Karthik}} = 7.69\,m/s\]

We see, the velocity of Karthik is more than the velocity of Arun. Therefore, obviously Karthik ran faster than Arun.

Note:
To finish the race, at each instant of time, the velocity of Karthik is greater than the velocity of Arun. Both Arun and Karthik started the race with initial velocity zero, but Karthik gained more acceleration than the acceleration of Arun which helped him to finish the match earlier than Arun.