car covers two fifths of a 150-km road with a velocity of 60 km/h east and then continues to cover
the rest towards the east in another hour. Find its average speed and average velocity (in km/h).
Answers
Answer:
Letx consider, x= total distance covered by the car,
Time taken to complete the half distance with velocity v=40km/h,
t
1
=
2×40
x
=
80
x
hr. . . . .(1)
The time taken to complete another half distance with velocity u=60km/h
t
2
=
2×60
x
=
120
x
hr
The total time taken, t=t
1
+t
2
t=
80
x
+
120
x
=
48
x
hr
The average speed of the car,
v
avg
=
x/48
x
=48km/h
The correct option is B.
Given
- A car covers ⅖th of its journey with a velocity of 60 km/h
- Total Distance = 150 km
To Find
- Average Speed & Average Velocity
Solution
☯ We know that Average Velocity is the same as Average speed in this case as it is given a road we assume it to be the shortest distance as well. But this is not applicable for all cases
✭ Distance covered in case 1
➞ Distance = ⅖ × 150
➞ Distance = 2 × 30
➞ Distance = 60 km
✭ Time taken in Case 1
➞ Speed = Distance/Time
➞ 60 = 60/Time
➞ Time = 60/60
➞ Time = 1 hour
━━━━━━━━━━━━━━━━━━━━━━━━━
✭ According to the Question :
- Time in case 2 = 1 hour
➞ Total Time = 1 + 1
➞ Total Time = 2 hours
Therefore,
- Avg Speed = Total Distance/Total Time
- Avg Speed = 150/2
- Avg Speed = 75 km/h