Question

A car moves with a speed of $40\text{ km/h}$ for $\text{15}$ minutes and then with a speed of $60\text{ km/h}$ for the next $\text{15}$ minutes. The total distance covered by the car is:
A. $35$
B. $25$
C. $45$
D. $66$

Answer 1

The distance d covered by a body, moving with speed s, in time t is given by $d=s\times t$

Complete step by step solution:
Let ${{d}_{1}}$ distance be covered in the first $\text{15}$ minutes when the car travels with a speed ${{s}_{1}}$ (say).
The speed of the car for the first $\text{15}$ minutes is $40\text{ km/h}$, so ${{s}_{1}}=40\text{ km/h}$
Convert the speed from km/h to metre per second using the conversion ratio $1\text{ km/h}=\dfrac{1000\text{ }}{3600\text{ }}\text{m/s}$
Therefore,
${{s}_{1}}=40\text{ km/h}=40\times \dfrac{1000\text{ }}{3600\text{ }}\text{ m/s} \\\ {{s}_{1}}=11.11\text{ m/s} \\\$
Substituting ${{s}_{1}}=11.11\text{ m/s}$ and ${{t}_{1}}\text{=15 min}\times 60\text{ s}=900\text{ s}$ in the distance formula, the distance covered in first $\text{15}$ minutes is
${{d}_{1}}={{s}_{1}}\times {{t}_{1}} \\\ \implies {{d}_{1}}=11.11\text{ m/s}\times \text{900 s} \\\ \implies {{d}_{1}}=9999\text{ m} \\\ \implies {{d}_{1}}\cong 10\text{ km} \\\$

Let ${{d}_{2}}$ distance be covered in the next $\text{15}$ minutes when the car travels with a speed ${{s}_{2}}$ (say).
Now, the speed of the car for the next $\text{15}$ minutes is $60\text{ km/h}$, so ${{s}_{2}}=60\text{ km/h}$
Convert the speed from km/h to metre per second using the conversion ratio $1\text{ km/h}=\dfrac{1000\text{ }}{3600\text{ }}\text{m/s}$
${{s}_{2}}=60\text{ km/h}=60\times \dfrac{1000\text{ }}{3600\text{ }}\text{ m/s} \\\ {{s}_{2}}=16.67\text{ m/s} \\\$
Substituting ${{s}_{2}}=16.67\text{ m/s}$ and ${{t}_{2}}\text{=15 min}\times 60\text{ s}=900\text{ s}$ in the distance formula, the distance covered in next $\text{15}$ minutes is
${{d}_{2}}={{s}_{2}}\times {{t}_{2}} \\\ \implies {{d}_{2}}=16.67\text{ m/s}\times \text{15 min} \\\ \implies {{d}_{2}}=16.67\text{ m/s}\times \text{900 s} \\\ \implies {{d}_{2}}=15003\text{ m} \\\ \implies {{d}_{2}}\cong 15.0\text{ km} \\\$
Therefore total distance travelled by the car in $\text{30}$ minutes is
$d={{d}_{1}}+{{d}_{2}} \\\ \implies d=10\text{ km}+15\text{ km} \\\ \therefore d=25\text{ km} \\\$

So, the total distance travelled by the car is $25\text{ km}$.

Therefore, option B is the correct answer.

Additional information: As the speed increases after the first fifteen minutes, the car is accelerating.

Note: It is important that the distance, speed and time be in the same system of units, preferably the S.I. unit system.
The problem can also be solved by plotting a speed-time graph. Either convert speed into m/s and time into seconds, or convert only time into hours and plot the speed-time graph. Take the car to be initially at rest.