Question

7.     

An engineer is designing the runway for

an airport. Of the planes that will use the airport, the lowest acceleration

rate is likely to be 2.50 m/s^2. The takeoff speed for this plane

will be 70.00 m/s. Assuming this minimum acceleration, what is the minimum

allowed length for the runway?

8.     

It was once recorded that a Jaguar left

skid marks that were 270.00 m in length. Assuming that the Jaguar skidded to a

stop with a constant acceleration of -3.60 m/s^2, determine the speed

of the Jaguar before it began to skid.

9.     

A speedboat increases its speed

uniformly from 20 m/s to 30 m/s in a distance of 300m. Find the time it take

the boat to travel the 300 m distance.

Answer 1

7. Using one of the kinematic formulas (see https://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic-formulas/a/what-are-the-kinematic-formulas), find the distance:

$$d = \dfrac{v^2-v_0^2}{2a}$$

where $v = 70.00m/s$ is the final speed, $v_0 = 0$ is the initial speed (assuming start from rest), and $a = 2.50m/s^2$ is the acceleration. Thus, obtain:

$$d = \dfrac{70^2-0^2}{2\cdot 2.5} =980m$$

8. Using the same equation, let's express now $v_0$ and substitute $v=0$ (final speed zero, came to rest), $d = 270.00m$ and $a = -3.60m/s^2$:

$$v_0 = \sqrt{-2ad}\\ v_0 = \sqrt{-2\cdot 270m\cdot (-3.6m/s^2)} \approx 44.1m/s$$

9. Using the different kinematic equation, obtain:

$$d = \dfrac{v+v_0}{2}t$$

where $d=300m,v = 30m/s,v_0=20m/s$ and $t$ is the required time. Expressing time, find:

$$t = \dfrac{2d}{v + v_0} = \dfrac{2\cdot 300m}{30m/s + 20m/s} = 12s$$

Answer. 7) 980m, 8) 44.1m/s, 9) 12s.