A body starts from rest from the origin with an acceleration of `6m//s^(2)` along x axis and `8m//s^(2)` along y axis.The distance from origin after 4 seconds will be

Options

A. 56m
B. 64m
C. 80m
D. 128m

Explanation

To solve the problem step by step, we will calculate the distance traveled by the body along the x-axis and y-axis separately, and then use the Pythagorean theorem to find the total distance from the origin.

### Step 1: Calculate the distance traveled along the x-axis
The formula for distance traveled under constant acceleration is given by:
\[ s_x = ut + \frac{1}{2} a_x t^2 \]
Where:
- \( s_x \) = distance traveled along the x-axis
- \( u \) = initial velocity (which is 0 since the body starts from rest)
- \( a_x \) = acceleration along the x-axis (6 m/s²)
- \( t \) = time (4 seconds)

Substituting the values:
\[ s_x = 0 \cdot 4 + \frac{1}{2} \cdot 6 \cdot (4^2) \]
\[ s_x = 0 + \frac{1}{2} \cdot 6 \cdot 16 \]
\[ s_x = 3 \cdot 16 = 48 \text{ meters} \]

### Step 2: Calculate the distance traveled along the y-axis
Using the same formula for the y-axis:
\[ s_y = ut + \frac{1}{2} a_y t^2 \]
Where:
- \( s_y \) = distance traveled along the y-axis
- \( a_y \) = acceleration along the y-axis (8 m/s²)

Substituting the values:
\[ s_y = 0 \cdot 4 + \frac{1}{2} \cdot 8 \cdot (4^2) \]
\[ s_y = 0 + \frac{1}{2} \cdot 8 \cdot 16 \]
\[ s_y = 4 \cdot 16 = 64 \text{ meters} \]

### Step 3: Calculate the total distance from the origin
To find the total distance from the origin, we can use the Pythagorean theorem:
\[ d = \sqrt{s_x^2 + s_y^2} \]
Substituting the values we found:
\[ d = \sqrt{(48)^2 + (64)^2} \]
\[ d = \sqrt{2304 + 4096} \]
\[ d = \sqrt{6400} \]
\[ d = 80 \text{ meters} \]

### Final Answer
The distance from the origin after 4 seconds is **80 meters**.

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