an aeroplane touches down on the landing strip at an airpot.Assume that the speed at which the plane touches down is 100m.s and that the maximum length of the runway is 1000m.calculate the average acceleration that the plane must stop within the length of the runway

Vf^2=Vi^2+2ad solve for a

To calculate the average acceleration, we need to use the formula:

acceleration = (final velocity - initial velocity) / time

In this case, the final velocity is 0 m/s because the plane needs to come to a complete stop. The initial velocity is 100 m/s (given in the problem), and we need to find the time it takes for the plane to stop.

We can rearrange the formula to solve for time:

time = (final velocity - initial velocity) / acceleration

Since the final velocity is 0 m/s, the equation becomes:

time = -initial velocity / acceleration

Now, plug in the values we know:

time = -100 m/s / acceleration

To find acceleration, we need to rearrange the formula once more:

acceleration = -initial velocity / time

Substituting the values:

acceleration = -100 m/s / time

Now, we know that the distance (length of the runway) is 1000 m, and we can relate this to time using the formula:

distance = initial velocity * time + (1/2) * acceleration * time^2

Since the plane stops at the end of the runway, the distance is equal to the length of the runway:

1000 m = 100 m/s * time + (1/2) * acceleration * time^2

Simplifying the equation:

1000 m = 100 m/s * time + (1/2) * (-100 m/s / time) * time^2

Simplifying further:

1000 m = 100 m/s * time - 50 m/s * time

Combining like terms:

1000 m = 50 m/s * time

Rearranging the equation to solve for time:

time = 1000 m / 50 m/s = 20 s

Now, substitute the time value back into the acceleration formula:

acceleration = -100 m/s / time = -100 m/s / 20 s = -5 m/s^2

Therefore, the average acceleration that the plane must stop within the length of the runway is -5 m/s^2 (negative because it represents deceleration or slowing down).