A car starts accelerating from rest to a velocity of 20 m/s in 10 min, maintains the velocity for 4 min and then comes to rest with uniform deceleration in 3 min. Draw the v–t graph. Also calculate the total distance travelled by the car.
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When we draw the graph we find that the motion is in form of a trapezium.
To calculate the distance we should understand that the area under the graph equals to distance.
This is because it is a graph of velocity against time and since distance equals to speed × time, we get the area.
In calculating the area we must understand that the time is in minutes and must be converted to seconds.
AREA :
We divide the trapezium into two triangles and one rectangle.
Areas of the figures are as follows :
Triangle one (during acceleration) :
0.5 × 20 × 600 = 6000 m
Triangle 2 (during declaration) :
0.5 × 20 × 180 = 1800 m
Rectangle (constant speed) :
20 × 40 = 800 m
Total distance :
6000 + 1800 + 800 = 8600 m
I have attached the diagram.
To calculate the distance we should understand that the area under the graph equals to distance.
This is because it is a graph of velocity against time and since distance equals to speed × time, we get the area.
In calculating the area we must understand that the time is in minutes and must be converted to seconds.
AREA :
We divide the trapezium into two triangles and one rectangle.
Areas of the figures are as follows :
Triangle one (during acceleration) :
0.5 × 20 × 600 = 6000 m
Triangle 2 (during declaration) :
0.5 × 20 × 180 = 1800 m
Rectangle (constant speed) :
20 × 40 = 800 m
Total distance :
6000 + 1800 + 800 = 8600 m
I have attached the diagram.
Attachments:
Pranothi1:
Why did u multiply 40 with 20?
Answered by
2
Answer:
Explanation:
When we draw the graph we find that the motion is in form of a trapezium.
To calculate the distance we should understand that the area under the graph equals to distance.
This is because it is a graph of velocity against time and since distance equals to speed × time, we get the area.
In calculating the area we must understand that the time is in minutes and must be converted to seconds.
AREA :
We divide the trapezium into two triangles and one rectangle.
Areas of the figures are as follows :
Triangle one (during acceleration) :
0.5 × 20 × 600 = 6000 m
Triangle 2 (during declaration) :
0.5 × 20 × 180 = 1800 m
Rectangle (constant speed) :
20 × 40 = 800 m
Total distance :
6000 + 1800 + 800 = 8600 m
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