An object starting from rest travels 77 m in the sixth second. What is its acceleration?

Since the object started from rest, the initial velocity is 0 m/s.

Using the equation, v = u + at (where, v is final velocity, a is the acceleration, t is time and u is the initial velocity), the velocity at the end of 5 seconds is given as:

v5 = 0 + a (5) = 5a m/s

Similarly, the velocity the end of 6 seconds is given as:

v6 = 0 + a(6) = 6a m/s

It is also given that the object traveled 77 m in the sixth second, which also means that the average velocity of the object was 77 m/s in the sixth seconds.

That is, (v5 + v6)/2 = 77 m/s

Substituting the values of v5 and v6 in the equation, we get:

(5a + 6a)/2 = 77 

or, 11a = 2 x 77 

or, a  = 14 m/s^2.

Thus, the acceleration of the object is 14 m/s^2.

Hope this helps.