Question

6. We want to design an airport runway with the following specifications. The lowest acceleration of a plane should be 4 m/s² and its take-off speed is 75 m/s. How long would the runway be to allow the planes to accelerate through it? 

7. An object moving with a slowing acceleration along a straight line. After 10s and covering a distance of 60m, its velocity reaches 4m/s. What is its initial velocity?

8. Suppose the position of a particle is given by s (t) = 1 + 3t - 2t², where t is in second and s is in meters.

a.    Find the displacement using the time interval between t = 1 and t = 3.

b.    Find the average velocity during the same time interval.

Answer 1

6) The distance is

$$d=v^2/(2a)=703\text{ m}.$$

7) Write a system of equations to find the initial velocity:

$$-60=v_0t-\frac{at^2}{2}=10v_0-50a,\\ 4=v_0-10a.\\\space\\ v_0=6.5\text{ m/s},\\ a=0.25\text{ m/s}^2.$$

8) The displacement:

$$s(3)-s(1)=(1+3·3-2·3^2)-(1+3·1-2·1^2)=-10\text{ m}.$$

The average velocity:

$$v_{av}=\frac{s(3)-s(1)}{3-1}=-5\text{ m/s}.$$