Question

a plane has take off speed of 88.3 m/s and requires 1365 m to reach that speed. determine the acceleration of the plane and the taken to reach the take off speed.

Answer 1

You can get a start on this problem by using four symbols:
t = time from start (at rest) to reaching takeoff speed
a = acceleration of plane (assumed to be constant, which may be an unrealistic assumption for an actual plane, but is probably what the problem asker expects)
v = takeoff speed of the plane
x = distance from start point to where plane reaches takeoff speed

Some equations you know from your course:
v = a*t speed reached after t seconds at acceleration a meters/sec^2
x = (v/2)*t = (1/2)*a*t^2 distance reached after t seconds, at an average velocity of v/2 for t seconds, or at a constant acceleration a for t seconds (you can use either equation).

And some numerical facts given to you in the problem:
v = 88.3 meters/sec
x = 1365 meters

So now you can plug ithe v and x values nto the above equations, and get two equations involving unknowns a and t. Then figure out the values of a and t.

Best wishes!