Example 4.6 provides a nice example of the overlap between kinematics and dynamics. it is known that the plane accelerates from rest to a take-off speed of 70 m/s over a distance of 940 m. use of the kinematic equation (vx)2f=(vx)2i+2axδx to find the acceleration of the plane, and then answer the following question. how long does it take the plane to reach its take-off speed?

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Explanation:

The acceleration of the plane can be determined by means of the kinematic equation that correspond to a Uniformly Accelerated Rectilinear Motion.

(1)

Where is the final velocity, is the initial velocity, is the acceleration and   is the distance traveled.

Equation (1) can be rewritten in terms of ax:

 (2)

Since the plane starts from rest, its initial velocity will be zero ():

Replacing the values given in equation 2, it is gotten:

So, The acceleration of the plane is    

Now that the acceleration is known, the next equation can be used to find out the time:

(3)

Rewritten equation (3) in terms of t:

Hence, the plane takes 26.92 seconds to reach its take-off speed.

c. magnitude and direction