Distance Travelled by a Jet Plane Before Stopping – Complete Theory and Detailed Solution

Concept Used

For motion with constant acceleration, the equations of motion (also called SUVAT equations) are used. Since the initial velocity, final velocity, and time are known, the most convenient equation for finding displacement is:

::contentReference[oaicite:0]{index=0}

First, calculate the acceleration using the first equation of motion:

v = u + at

Step 1: Calculate the Acceleration

Substituting the given values,

0 = 70 + a × 3

3a = -70

a = -70/3 m/s²

a ≈ -23.33 m/s²

The negative sign indicates that the plane is decelerating.

Step 2: Calculate the Distance Travelled

Now use the second equation of motion:

s = ut + ½at²

Substituting the values,

s = (70 × 3) + ½ × (-70/3) × (3)²

s = 210 – 105

s = 105 m

Therefore, the jet plane travels a distance of 105 metres before coming to rest.

Alternative Short Method

We can also use the average velocity because the acceleration is constant.

Average velocity

= (u + v)/2

= (70 + 0)/2

= 35 m/s

Distance travelled

= Average velocity × Time

= 35 × 3

= 105 m

This method is much faster and is highly useful in objective-type examinations.

Why Does the Plane Stop Uniformly?

The question states that the acceleration is constant. This means the braking force acting on the aircraft remains approximately constant during the stopping interval. As a result, the velocity decreases uniformly with time, allowing the equations of uniformly accelerated motion to be applied directly.

Real-Life Applications

The concept of stopping distance is extremely important in aviation, automobile engineering, and transportation safety. Aircraft carriers use arresting cables to stop fighter jets within a very short distance. Engineers calculate the required stopping distance to ensure that the aircraft comes to rest safely without overshooting the runway.

The same principles are also used to determine the braking distance of cars, trains, and high-speed vehicles.

Important Formulae

First Equation of Motion

v = u + at

Second Equation of Motion

s = ut + ½at²

Third Equation of Motion

v² = u² + 2as

Average Velocity

Average Velocity = (u + v)/2

Distance Using Average Velocity

s = Average Velocity × Time

Key Points to Remember

Whenever a body moves with constant acceleration or deceleration, the equations of motion provide the simplest way to calculate displacement, velocity, acceleration, or time. If the initial and final velocities are known, using the average velocity method often saves time during competitive examinations.

Final Answer

The jet plane travels a distance of

105 m