**Solution:**

Let's assume the initial velocity of the particle is v m/s and the rate of change of velocity is a m/s².

**Calculating the velocity at the 6th second:**
The rate of change of velocity is constant, so the velocity at the 6th second can be calculated using the formula:

v6 = v + a * t

where v6 is the velocity at the 6th second, v is the initial velocity, a is the rate of change of velocity, and t is the time in seconds.

**Calculating the velocity at the 11th second:**
Similarly, the velocity at the 11th second can be calculated using the same formula:

v11 = v + a * t

where v11 is the velocity at the 11th second, v is the initial velocity, a is the rate of change of velocity, and t is the time in seconds.

**Finding the position at the 6th second:**
The position at the 6th second can be calculated using the formula:

s6 = v * t + (1/2) * a * t²

where s6 is the position at the 6th second, v is the initial velocity, a is the rate of change of velocity, and t is the time in seconds.

**Finding the position at the 11th second:**
Similarly, the position at the 11th second can be calculated using the same formula:

s11 = v * t + (1/2) * a * t²

where s11 is the position at the 11th second, v is the initial velocity, a is the rate of change of velocity, and t is the time in seconds.

**Equating the positions at the 6th and 11th second:**
Since it is given that the position at the 6th second is the same as the position at the 11th second, we can equate the two equations:

s6 = s11

v * 6 + (1/2) * a * (6)² = v * 11 + (1/2) * a * (11)²

**Simplifying the equation:**
v * 6 + 18a = v * 11 + 60.5a

Simplifying further, we get:

5v = 42.5a

**Finding the time when the particle returns to its starting point:**
To find the time when the particle returns to its starting point, we need to find the value of t for which the position is zero. Using the formula for position:

s = v * t + (1/2) * a * t²

We can substitute s = 0 into this equation and solve for t:

0 = v * t + (1/2) * a * t²

0 = t(v + (1/2) * a * t)

Either t = 0 or v + (1/2) * a * t = 0

Since the particle is already in motion, t cannot be zero. Therefore, we solve the equation:

v + (1/2) * a * t = 0

t = -2v / a

So, the particle returns to its starting point at time t = -2v / a.

Is ans t=17 sec right.