Question

.7
A body starting from rest with an acceleration 20
cm/s². What is the distance covered by the body
in first 8 seconds?

Answer 1

Certainly! Let's solve the problem step-by-step.

### Given Data:
- The body starts from rest, so the initial velocity (u) is 0 cm/s.
- The acceleration (a) is 20 cm/s².
- The time duration (t) is 8 seconds.

### To Find:
The distance covered by the body in the first 8 seconds.

### Approach:
We can use one of the kinematic equations of motion, which relates distance, initial velocity, acceleration, and time. The equation is:

$\[ \text{distance} = u \cdot t + \frac{1}{2} \cdot a \cdot t^2 \]$

Where:
- $\( u \)$ is the initial velocity.
- $\( a \)$ is the acceleration.
- $\( t \)$ is the time duration.

### Step-by-Step Solution:

1. Initial Velocity (u):
Since the body starts from rest:
$\[ u = 0 \, \text{cm/s} \]$

2. Acceleration (a):
Given:
$\[ a = 20 \, \text{cm/s}^2 \]$

3. Time (t):
Given:
$\[ t = 8 \, \text{seconds} \]$

4. Plug the Values into the Equation:
Now we need to substitute the known values into the kinematic equation:
$\[ \text{distance} = 0 \cdot 8 + \frac{1}{2} \cdot 20 \cdot 8^2 \]$

5. Calculate the Distance:
$\[ \text{distance} = 0 + \frac{1}{2} \cdot 20 \cdot 64 \]$
$\[ \text{distance} = 10 \cdot 64 \]$
$\[ \text{distance} = 640 \]$

### Final Answer:
The distance covered by the body in the first 8 seconds is 640 cm.