A particle starting from rest attains a velocity of `50 ms^(-1)` in 5 s. The acceleration of the particle is

Options

A. `5 m/s^2`
B. `10 m/s^2`
C. `50 m/s^2`
D. `100 m/s^2`

Answer

To find the acceleration of the particle, we can use the first equation of motion, which relates initial velocity, final velocity, acceleration, and time. Here's the step-by-step solution:

### Step 1: Identify the given values
- Initial velocity (u) = 0 m/s (since the particle starts from rest)
- Final velocity (v) = 50 m/s
- Time (t) = 5 s

### Step 2: Write down the first equation of motion
The first equation of motion is:
\[ v = u + at \]
where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ 50 = 0 + a \cdot 5 \]

### Step 4: Simplify the equation
This simplifies to:
\[ 50 = 5a \]

### Step 5: Solve for acceleration (a)
To find \( a \), divide both sides of the equation by 5:
\[ a = \frac{50}{5} \]

### Step 6: Calculate the acceleration
Calculating the right side gives:
\[ a = 10 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the particle is \( 10 \, \text{m/s}^2 \).

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