A car moves first 0.1 hours with velocity 20km/h then for 0.4 hour with a velocity 60km/h and in the last for 0.2 hours with a velocity of 20km/h. Draw time-velocity graph for the car and use it to find
1) how much distance the car moves in the first time interval
2) how much distance the car moves in the whole journey
3)how much time the car takes in the first 14 km also indicate the area covered in your map
Answers
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We know that
Velocity(V) = Displacement(S) / time(t) taken
1) Time taken = 0.1 hr
Velocity = 20km/hr
so, Distace = V × t
= 20× 0.1 km
= 2 km
2) Distance travelled by car in whole journey.
Average velocity = (V1+ V2 +V3) / 3
=(20+60+20)/3 km/hr
= 100/3 km/hr
Total time taken =( .1)+ (.4) +(.2) hr
= .7 hr
So, Total distance travel = Average velocity×Total time taken
=100/3 × .7 km
= 70/3 km
= 23.33 km
3) Time taken by car in first 14 km
=Distance / Average velocity
= 14 / (100/3)
= 14×3 /100
= 42/100
= .42 hr
The total distance traveled in the first interval by car is 2 km.
The total distance traveled by car in the whole journey is 30km.
The time taken by the car in the first 14 km is 0.3 hours.
Given:
For t₁ = 0.1 hr, the velocity of the car, v₁ = 20 km/hr
For t₂ = 0.4 hr , the velocity of car, v₂ = 60 km/hr
For t₃ = 0.2 hr, the velocity of car, v₃ = 20 km/hr
To Find:
The distance traveled in the first interval and in the whole journey.
The time taken by the car to cover 14 km and the area covered on the map.
Solution:
We are required to find the distance, time, and area covered by the car by using the graph inserted.
We know the area of the velocity-time graph gives the distance traveled.
1) For the distance traveled in the first interval(0-0.1 hr),
From the graph, find the area of the A1 section which is in a rectangle shape so the area is length×breadth
Area of A1 section = length×breadth
= 0.1×20
= 2 km
Therefore, The total distance traveled in the first interval by car is 2 km.
2) For the distance traveled in the whole journey(0-0.7 hr),
From the graph, find the area of the A1, A2, and A3 sections which is in a rectangle shape so the area is length×breadth
Area of A1 section = length×breadth
= 0.1×20
= 2 km
Area of A2 section = length×breadth
= (0.5-0.1)×60
= 0.4×60
= 24 km
Area of A3 section = length×breadth
= (07-0.5)×20
= 0.2×20
= 4 km
Total distance = total area(A1+A2+A3)
= 2+24+4
= 30 km
Therefore, The total distance traveled by car in the whole journey is 30km.
3) The car travels 2 km in 0.1 hr at the first interval then the remaining distance is (14-2) = 12 km
t₁ = 0.1hr
We know, time = distance/ velocity ------(1)
Here the car travels the next 24 km at 60 km/hr so for the distance of 12 km the car traveled at 60km/hr
On applying v = 60 km/hr and d = 12 km in equation(1)
t₂ = 12/60
= 0.2 hr
Total time (t) = t₁+t₂
= 0.1+0.2
= 0.3 hr
Therefore, The time taken by the car in the first 14 km is 0.3 hours.
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