Answer to Question #157475 in Physics for John Peter

Question

1. The human body can survive an acceleration of less than 250 m/s2. If a person is involved in a car accident with a velocity of 110 km/h and is stopped by an airbag, over what distance must the air bag stop the person to survive the crash.

2. Suppose your electric bicycle (e-bike) is at rest and can reach a velocity of 12 m/s in 9s Assuming that it accelerates at a constant rate; what is its acceleration in m/s2?

3. Consider a jeepney at rest in the terminal accelerates at a constant acceleration of 4.5m/s^2

a. what is the velocity after 7?

b.) how much distance did the jeepney travel at this time

Answer 1

1)

$$v^2=v_0^2+2ad,$$ $$d=\dfrac{v^2-v_0^2}{2a},$$ $$d=\dfrac{0-(110\ \dfrac{km}{h}\cdot\dfrac{1000\ m}{1\ km}\cdot\dfrac{1\ h}{3600\ s})^2}{2\cdot(-250\ \dfrac{m}{s^2})}=1.86\ m.$$

2)

$$a=\dfrac{v-v_0}{t}=\dfrac{12\ \dfrac{m}{s}}{9\ s}=1.33\ \dfrac{m}{s}.$$

3)

a)

$$v=at=4.5\ \dfrac{m}{s^2}\cdot7\ s=31.5\ \dfrac{m}{s}.$$

b)

$$d=v_0t+\dfrac{1}{2}at^2=\dfrac{1}{2}\cdot4.5\ \dfrac{m}{s^2}\cdot(7\ s)^2=110.25\ m.$$