Problem: A car covers first 50 km at a uniform velocity of 45 km/h and the next 50 km at 90 km/h .Find the average velocity of the car.

Solution:

To find the average velocity of the car, we need to use the following formula:

Average Velocity = Total Distance Covered / Total Time Taken

Let's start by finding the time taken by the car to cover the first 50 km at a uniform velocity of 45 km/h:

Time taken = Distance / Velocity
Time taken = 50 km / 45 km/h
Time taken = 1.11 hours

Similarly, let's find the time taken by the car to cover the next 50 km at a velocity of 90 km/h:

Time taken = Distance / Velocity
Time taken = 50 km / 90 km/h
Time taken = 0.56 hours

Now, let's find the total time taken by the car:

Total time taken = Time taken for first 50 km + Time taken for next 50 km
Total time taken = 1.11 hours + 0.56 hours
Total time taken = 1.67 hours

Finally, let's find the total distance covered by the car:

Total distance covered = Distance covered in first 50 km + Distance covered in next 50 km
Total distance covered = 50 km + 50 km
Total distance covered = 100 km

Now, we can use the formula to find the average velocity of the car:

Average Velocity = Total Distance Covered / Total Time Taken
Average Velocity = 100 km / 1.67 hours
Average Velocity = 59.88 km/h

Therefore, the average velocity of the car is 59.88 km/h.

V aver =total dis/total time. 50+50/50/45+50/90=100/1.66=60km/h*5/18=16.6m/s