a jet plane starts from rest with an acceleration of 3 m/s^2 and makes a run for 35 sec before taking off .What is the minimum length of the runway and what is the velocity of the jet at the take off ?

s = 1/2 at^2 = 1/2 * 3 * 35^2

v = at = 3 * 35

To find the minimum length of the runway, we need to calculate the distance covered by the jet during the acceleration phase.

We can use the formula:

distance = (acceleration * time^2) / 2

Given that the acceleration is 3 m/s^2 and the time is 35 seconds, we can calculate the distance:

distance = (3 * 35^2) / 2
= (3 * 1225) / 2
= 3675 / 2
= 1837.5 meters

So, the minimum length of the runway is 1837.5 meters.

Next, we can calculate the velocity of the jet at takeoff using the formula:

velocity = acceleration * time

Given that the acceleration is 3 m/s^2 and the time is 35 seconds, we can calculate the velocity:

velocity = 3 * 35
= 105 m/s

Therefore, the velocity of the jet at takeoff is 105 m/s.

To find the minimum length of the runway and the velocity of the jet at takeoff, we can use the equations of motion.

1. Calculate the final velocity of the jet at takeoff (v):

We can use the equation of motion: v = u + at
where,
v = final velocity of the jet (which is what we need to find),
u = initial velocity of the jet (which is 0 m/s, as it starts from rest),
a = acceleration of the jet (given as 3 m/s^2),
t = time taken for the run (35 sec).

Substituting the given values:
v = 0 + (3 m/s^2) * (35 sec)
v = 0 + 105 m/s
v = 105 m/s

Therefore, the velocity of the jet at takeoff is 105 m/s.

2. Calculate the minimum length of the runway (s):

We can use the equation of motion: s = ut + (1/2)at^2
where,
s = distance covered during the run (which is what we need to find),
u = initial velocity of the jet (0 m/s),
a = acceleration of the jet (3 m/s^2),
t = time taken for the run (35 sec).

Substituting the given values:
s = (0 m/s) * (35 sec) + (1/2) * (3 m/s^2) * (35 sec)^2
s = 0 + (1/2) * (3 m/s^2) * (1225 sec^2)
s = (1/2) * 3675 m^2/s^2
s = 1837.5 m

Therefore, the minimum length of the runway is 1837.5 meters.

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