A car travels a certain distance with a speed of
50 km/her & returns with a speed of 40 km/her
Calculate
the
average
speed
average. velocity of the car
for whole journey
(15)
Answers
Question
A car travels a certain distance with a speed of 50 km/her & returns with a speed of 40 km/her. Calculate the average speed and average velocity of the car for whole journey.
Solution
Average speed is defined as the ratio of total distance covered with respect to total time taken. Whereas average velocity is defined as the total displacement with respect to total time taken.
A car travels a certain distance with a speed of 50 km/her & returns with a speed of 40 km/her.
S1 = 50 km/hr and S2 = 40 km/hr
Average speed = (2 × S1 × S2)/(S1 + S2)
= (2 × 50 × 40)/(50 + 40)
= 4000/90
= 44.44
Therefore, the average speed of the car is 44.44 km/hr.
There is one more way to find the average speed. For that, first of all we have to find the time using S1 then for S2. And we have to make a assumption too, that the distance covered by the car is x km.
Then, total distance covered = 2x km and total time taken = t1 + t2
On solving we get, average speed 44.44 km/hr.
Since, the initial and final points of the car are same. So, the total displacement of the car is zero.
Therefore, the average velocity of the car is 0 km/hr.
Case-1,
⇝ Let the car travels from A to B, and covers a distance of x km. The speed of the car while moving from A to B is 50 km/h.
Let the time taken be t1.
⤷ t1 = x/50 hours
Case-2,
⇝ When the car returns from B to A, the distance covered remains x km. The speed of the car while moving from B to A is 40 km/h.
Let the time taken be t2.
⤷ t2 = x/40 hours
We know,
✪ Average speed = Total distance travelled/Total time taken
✪ Average velocity = Total displacement/Total time taken
Total time taken(t) = (x/50) + (x/40) hrs
⇒t = (4x + 5x)/200
⇒t = 9x/200 hrs
______________
Total distance travelled = x + x = 2x km.
Total time taken = 9x/200 hrs
Average speed = 2x ÷ (9x/200)
⇒Average speed = 2x × 200/9x
⇒Average speed = 400/9
⇒Average speed = 44·44 km/h
______________
Total displacement = 0
(As the starting point and the final position, i.e. A are the same)
Total time taken = 9x/200 hrs
Average velocity = Total displacement/Total time taken
⇒Average velocity = 0 ÷ 9x/200