A car travels from stop A to stop B with a speed of 30 km/h and then returns to A with a speed of 50 km/h. Find a) displacement of the car. b) distance travelled by the car. c) average speed of the car.
Answers
A car travels from stop A to stop B with a speed of 30km/h and then returns back to stop A with a speed of 50km/h.
We have to find the-
(a) Displacement of the car.
(B) Distance travelled by the car.
(c) Average speed of the car.
Assume that the distance covered by the car is x km.
(a) Since the car starts from point A to B and then returns back to point A again using the same pathway. Final and initial of the car is same i.e. A point.
Therefore, the Displacement of the car is 0 km.
(B and c) Average speed is defined as the ratio of total distance covered with respect to total time taken.
As the distance covered by the car is same i.e. x km. From A to B distance covered is x km and from B to A distance covered is x km. So, the total distance covered by the car is 2x km.
Also,
Time = Distance/Speed
t1 = x/30 hr and t2 = x/50 hr
Total time taken = t1 + t2
= x/30 + x/50
= x/5(4/15)
= 4x/75
Average speed = 2x/(4x/75)
= (2*75)/4
= 37.5
Therefore, the average speed of the car is 37.5 km/hr.
Given :
A car travels from stop A to stop B with a speed of 30 km/h and then returns to A with a speed of 50 km/h
To Find :
a) displacement of the car.
b) distance travelled by the car.
c) average speed of the car.
Solution :
a) displacement of the car
Given that , A car travels from stop A to B with a speed of 30 km/h and then returns to A with a speed of 50 km/h
So the initial and final positions are same .
We know that displacement is the shortest distance i.e., difference b/w final and initial positions .
⇒ Displacement of the car is zero .
b) distance travelled by the car
Let the distance covered by car to travel from stop A to B be " x "
So , distance b/w stop B to A is also " x "
Therefore the total distance travelled by car = Distance b/w stop A & B + Distance b/w stop B & A
⇒ Distance travelled by car = x + x = 2x
c) average speed of the car
Average Speed : It is defined as the total distance covered per total time .
Total Distance , D = 2x [ From b) ]
Time_A-B = Distance_A-B / Speed_A-B
⇒ Time_A-B = x / 30
Time_B-A = Distance_B-A / Speed_B-A
⇒ Time_B-A = x / 50
Now , Total Time , T = x / 30 + x / 50
⇒ T = 4 x / 75
Now , Average Speed = Total Distance , D / Total Time , T
⇒ A.Speed = 2x / ( 4 x / 75 )
⇒ A.Speed = 75/2
⇒ A. SPeed = 37.5 km/h
So the Average Speed of the car is 37.5 km/h