The displacement of a body in 8 s starting from rest with an acceleration of `20 cms^(-2)` is

Options

A. 64 m
B. 64 cm
C. 640 cm
D. `0.064 m`

Explanation

To solve the problem of finding the displacement of a body that starts from rest and accelerates at a constant rate, we can use the equations of motion. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Initial velocity (u) = 0 cm/s (since the body starts from rest)
- Acceleration (a) = 20 cm/s²
- Time (t) = 8 s

### Step 2: Use the equation of motion
We can use the second equation of motion for constant acceleration:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s \) = displacement
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

### Step 3: Substitute the known values into the equation
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ s = 0 \cdot t + \frac{1}{2} a t^2 \]
\[ s = \frac{1}{2} \cdot 20 \cdot (8)^2 \]

### Step 4: Calculate \( t^2 \)
Calculate \( t^2 \):
\[ t^2 = 8^2 = 64 \]

### Step 5: Substitute \( t^2 \) back into the equation
Now substitute \( t^2 \) back into the equation:
\[ s = \frac{1}{2} \cdot 20 \cdot 64 \]

### Step 6: Calculate the displacement
Calculate \( s \):
\[ s = \frac{1}{2} \cdot 20 \cdot 64 = 10 \cdot 64 = 640 \text{ cm} \]

### Step 7: Final answer
Thus, the displacement of the body in 8 seconds is:
\[ s = 640 \text{ cm} \]