A car travels a distance of 2000 m. If the first half distance is covered at 40km/hour and the second half at velocity v and if the average velocity is 48km/hour, then the value of v is -
Given,
Distance = 2000 m = 2 km [converted meter into kilometer]
Average Velocity = 48 km/hour
Velocity to cover the first half distance (1 km) = 40 km/h
Velocity to cover the second half distance = v
To find = v
Solution:
We know that,
$Time=\frac{Distance}{Speed}$
So, putting the value of speed and distance in the above equation, we'll get the time taken by the car to cover the first half distance.
$Time=\frac{1}{40}$
Repeating same as above we'll get the time taken by the car to cover the second half distance.
$Time=\frac{1}{v}$
Now, we know that-
Average $Average\ Speed=\frac{Total\ Distance}{Total\ Time}$
Substituting the given values in the above formula we get-
$48=\frac{2}{\frac{1}{40}+\frac{1}{v}}$
$48=\frac{2}{\frac{v+40}{40v}}$
$\frac{v+40}{40v}=\frac{2}{48}$
$\frac{v+40}{40v}=\frac{1}{24}$
$24(v+40)=40v$
$24v+960=40v$
$40v-24v=960$
$16v=960$
$v=\frac{960}{16}$
$v=60km/h$
Hence, the value of $v$ or the speed of the car in the second half is 60km/h.
Related Articles
- A car covers a distance of 101.25 km in 2.5 hours. What is the average distance covered by it in 1 hour
- If V is the variance and M is the mean of first 15 natural numbers then what is $V+M^{2}$ equal to ?
- A person travelled the first half of the journey with a velocity of \( 20 \mathrm{~m} / \mathrm{s} \) and the rest with a velocity of \( 30 \mathrm{~m} / \mathrm{s} \). Find the average velocity of the whole journey.
- A car acquires a velocity of 72 km per hour in 10 seconds starting from rest. Find the average velocity.
- A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
- A train can travel $200\ m$ in the first hour, $400\ m$ the next hour, $600\ m$ the third hour and so on in an arithmetic sequence. What is the total distance the train travels in $5$ hours?
- A car of mass $1000\ kg$ is moving with a velocity of $10\ m/s$. If the velocity-time graph for this car is a horizontal line parallel to the time axis, then the velocity of the car at the end of $25\ s$ will be:a). 40 m/s b). 25 m/sc). 10 m/s d). 250 m/s
- What is the momentum of an object of mass m, moving with a velocity v?
- If the value of three chocolates is Rs. 5 then what is the value of half chocolate?
- A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed, if it takes 3 hours to complete the total journey, what is its original average speed?
- A body is moving along a circular path of radius (r) with uniform speed (v) \n1 . What is the direction of instantaneous velocity? \n2. What is magnitude of average velocity in (I) half rotation and (ii) three fourth rotation\n3. What is the direction of instantaneous acceleration?
- A car moves a distance of 2592 km with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in km/hour. Find the time taken to cover the distance.
- A rocket is moving up with a velocity v. If the velocity of this rocket is suddenly tripled, what will be the ratio of two kinetic energies?
- A train travels at a certain average speed for a distance of $63\ km$ and then travels at a distance of $72\ km$ at an average speed of $6\ km/hr$ more than its original speed. It it takes $3\ hours$ to complete total journey, what is the original average speed ?
- If Boojho covers a certain distance in one hour and Paheli covers the same distance in two hours, who travels in a higher speed?
Kickstart Your Career
Get certified by completing the course
Get Started