The distance time graph of a particle at time `t` makes angle `45^(@)` with respect to time axis. After `1s`, if makes angle `60^(@)` with respect to time axis. What is the acceleration of the particle?

Options

A. `(sqrt(3)-1)` unit
B. `(sqrt(3)+1)` unit
C. `sqrt(3)` unit
D. `1 ` unit

Explanation

To solve the problem step-by-step, we will analyze the distance-time graph and calculate the acceleration of the particle based on the angles given.

### Step 1: Understand the relationship between slope and velocity
The slope of a distance-time graph represents the velocity of the particle. The angle made with the time axis can be used to calculate the slope using the tangent function.

### Step 2: Calculate the initial velocity (v1)
At time \( t = 0 \) seconds, the angle is \( 45^\circ \).
Using the tangent function:
...