A body starts from rest and moves with a uniform acceleration of `10ms^(-2)` for 5 seconds. During the next 10 seconds it moves with uniform velocity. Find the total distance travelled by the body (Using graphical analysis).

Options

A. `2 m//s^(2)`
B. `4 m//s^(2)`
C. `6 m//s^(2)`
D. None of these

Explanation

To solve the problem step by step, we will analyze the motion of the body using a velocity-time (v-t) graph.

### Step 1: Understand the Motion
The body starts from rest, which means the initial velocity \( u = 0 \). It accelerates uniformly with an acceleration \( a = 10 \, \text{m/s}^2 \) for \( t_1 = 5 \, \text{s} \). After this, it moves with a uniform velocity for \( t_2 = 10 \, \text{s} \).

### Step 2: Calculate the Final Velocity after Acceleration
Using the first equation of motion:
\[ v = u + at \]
Substituting the values:
\[ v = 0 + (10 \, \text{m/s}^2)(5 \, \text{s}) = 50 \, \text{m/s} \]
So, after 5 seconds, the final velocity \( v = 50 \, \text{m/s} \).

### Step 3: Sketch the Velocity-Time Graph
- The graph starts at the origin (0,0) since the body starts from rest.
- At \( t = 5 \, \text{s} \), the velocity reaches \( 50 \, \text{m/s} \). This creates a straight line from (0,0) to (5,50).
- For the next 10 seconds (from \( t = 5 \, \text{s} \) to \( t = 15 \, \text{s} \)), the body moves with a constant velocity of \( 50 \, \text{m/s} \). This is represented by a horizontal line from (5,50) to (15,50).

### Step 4: Calculate the Area Under the Graph
The total distance travelled by the body can be found by calculating the area under the v-t graph.

1. **Area of the Triangle (from 0 to 5 seconds)**:
- Base = 5 seconds
- Height = 50 m/s
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 50 = 125 \, \text{m} \]

2. **Area of the Rectangle (from 5 to 15 seconds)**:
- Base = 10 seconds
- Height = 50 m/s
\[ \text{Area}_{\text{rectangle}} = \text{base} \times \text{height} = 10 \times 50 = 500 \, \text{m} \]

### Step 5: Total Distance Travelled
Now, we add the areas of the triangle and the rectangle to find the total distance travelled:
\[ \text{Total Distance} = \text{Area}_{\text{triangle}} + \text{Area}_{\text{rectangle}} = 125 \, \text{m} + 500 \, \text{m} = 625 \, \text{m} \]

### Final Answer
The total distance travelled by the body is **625 meters**.

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