A car is moving along a straight road. The graph below shows how the speed
varies with time.
"'0
W
WCl.
(/)
time -
Which of the following graphs represents the distance covered by the car with
time?
I
1. t 2.
0>
U 0>
C
o
.l9 c
'"
.l9
ii .!!!
"0
time - time -
3. 4.
0>
U 0>
C
U
ro c
1!!
.l9
'"
"0 ii
time - time -
The correct graph representing the distance covered by the car with time would be graph number 2.
This is because, in the given speed-time graph, the speed of the car is initially increasing with time which means the distance covered will also increase at an increasing rate during that period, as seen in the initial upward curve in graph 2. Then, the speed becomes constant for some time, during which the distance covered will increase at a constant rate, shown by the straight line in graph 2. Finally, the speed decreases with time, which means the rate of distance covered will also decrease, as represented by the decreasing curve in graph 2.
To determine which of the given graphs represents the distance covered by the car with time, we need to understand the relationship between speed, time, and distance.
Distance covered can be found by calculating the area under the speed-time graph. This is because the area under the graph represents the distance traveled during that time interval.
Let's analyze each of the given graphs:
Graph 1:
- This graph represents a constant speed over time.
- Since the speed is constant, the distance covered would be represented by a straight line graph.
- This is not the correct graph because it does not change with time.
Graph 2:
- This graph represents speed increasing over time.
- As the speed increases, the distance covered per unit of time would also be increasing.
- This is the correct graph as the distance covered should increase with time.
Graph 3:
- This graph represents speed decreasing over time.
- As the speed decreases, the distance covered per unit of time would also be decreasing.
- This is not the correct graph as the distance covered should be increasing with time.
Graph 4:
- This graph represents speed varying irregularly over time.
- Since the speed is varying irregularly, it is difficult to determine the pattern of the distance covered.
- This is not the correct graph as it does not show a consistent relationship between distance and time.
So, the correct graph representing the distance covered with time is Graph 2.
To determine which graph represents the distance covered by the car with time, we need to understand the relationship between speed, time, and distance.
The speed of an object is defined as the rate at which it covers distance. Mathematically, speed is equal to the distance traveled divided by the time taken:
Speed = Distance / Time
If we rearrange this equation, we can determine the distance traveled:
Distance = Speed * Time
Since the graph given shows the speed of the car with time, we can use this information to find the distance covered by the car.
For each point on the graph, the value on the y-axis represents the speed of the car at a specific point in time. To calculate the distance covered at each point, we'll need to multiply the speed at that point by the time elapsed. Then, we can plot these calculated values on a new graph to represent the distance covered by the car with time.
Let's calculate the distance covered at each point for each given graph:
1. For graph 1, since the speed is constant at all times, the distance covered by the car will be the same for each point on the graph. Therefore, this graph represents a constant distance covered by the car with time.
2. For graph 2, the speed starts at zero and gradually increases with time. This means that the distance covered by the car increases as time goes by. We can see this by observing that the space between the speed curve and the time axis gradually increases. Therefore, this graph represents an increasing distance covered by the car with time.
3. For graph 3, the speed starts at a maximum value and gradually decreases with time, eventually reaching zero speed. This means that the car is decelerating. As the speed decreases, the distance covered by the car will still increase but at a decreasing rate. We can observe this by noting that the slope of the curve becomes less steep over time. Therefore, this graph represents a distance covered by the car that initially increases but at a decreasing rate.
4. For graph 4, the speed starts at zero and gradually increases to a maximum value before decreasing again to reach zero speed. This represents acceleration and then deceleration. As time increases, the distance covered by the car will initially increase more rapidly, and then increase more slowly as it starts decelerating. Therefore, this graph represents a distance covered by the car that initially increases at an increasing rate, and then increases at a decreasing rate.
Based on the explanations above, graph 2 represents the distance covered by the car with time, as it shows a consistent increase in distance as time goes by.