A body moves from rest with a uniform acceleration and travels 270 m in 3 s. Find the velocity of the body at 10 s after the start.

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the given information
- Initial velocity (u) = 0 m/s (the body starts from rest)
- Distance traveled (s) = 270 m
- Time taken (t) = 3 s

### Step 2: Use the equation of motion to find acceleration (a)
We can use the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]

Substituting the known values:
\[ 270 = 0 \cdot 3 + \frac{1}{2} a (3)^2 \]

This simplifies to:
\[ 270 = \frac{1}{2} a \cdot 9 \]
\[ 270 = \frac{9}{2} a \]

### Step 3: Solve for acceleration (a)
To isolate \( a \), multiply both sides by 2:
\[ 540 = 9a \]

Now, divide both sides by 9:
\[ a = \frac{540}{9} \]
\[ a = 60 \, \text{m/s}^2 \]

### Step 4: Find the velocity at 10 seconds
We will now use the first equation of motion to find the velocity (V) at t = 10 s:
\[ V = u + at \]

Substituting the known values:
\[ V = 0 + (60 \, \text{m/s}^2)(10 \, \text{s}) \]
\[ V = 600 \, \text{m/s} \]

### Final Answer
The velocity of the body at 10 seconds after the start is **600 m/s**.

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