The distance travelled by the moving body is :

Options

A. The area between the speed time graph and time axis.
B. The area between the speed time graph and speed axis
C. The area between the distance time graph and time axis
D. The area between the distance time graph and distance axis

Answer

To find the distance traveled by a moving body, we can use the relationship between distance, speed (or velocity), and time. Here’s a step-by-step solution:

### Step 1: Understand the relationship between distance, speed, and time
The fundamental relationship is given by the formula:
\[ \text{Distance} (s) = \text{Speed} (v) \times \text{Time} (t) \]

### Step 2: Identify the variables
- Let \( v \) be the speed of the moving body.
- Let \( t \) be the time for which the body is moving.
- The distance \( s \) can be calculated if we know the values of \( v \) and \( t \).

### Step 3: Use the integral for variable speed
If the speed is not constant, we need to integrate the speed over time to find the total distance traveled:
\[ s = \int v \, dt \]
This means we need to find the area under the speed-time graph.

### Step 4: Calculate the area under the curve
If we have a speed-time graph, the distance traveled can be found by calculating the area under the curve between the specified time limits (from \( t_0 \) to \( t_1 \)):
- For example, if the speed is constant, the area is simply a rectangle:
\[ \text{Area} = \text{Base} \times \text{Height} = t \times v \]
- If the speed varies, we may need to break the graph into shapes (like triangles, rectangles) and calculate the area accordingly.

### Step 5: Evaluate the integral
If we have specific values for speed over time, we can evaluate the integral:
\[ s = \int_{0}^{10} v \, dt \]
This will give us the total distance traveled from time \( t = 0 \) to \( t = 10 \) seconds.

### Conclusion
The distance traveled by the moving body can be calculated using the relationship between speed and time, and if the speed is variable, we can find the total distance by integrating the speed function over the given time interval.

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