Answer to Question #153776 in Mechanics | Relativity for Martha Cryer

Question

A nail is fired into a block of wood at a velocity of 200 m/s. If the deceleration is 2 million m/s² how far does the nail travel before it comes to a stop?

Answer 1

Solution:

Assuming that deceleration keeps constant during the braking process, we can use one of the kinematics equations, as follows:

$$v^2_f-v^2_o=2*a*(\Delta x)$$

where $v_f$ is the final velocity (0 in our case), $v_o$ is the initial velocity (200 $\tfrac{m}{s}$ ), decceleration (-2000000 $\tfrac{m}{s^2}$ ), and Δx is the distance traveled.

$\dfrac{}{}$

$$\Delta x=\dfrac{-v^2_o}{2*a}=\dfrac{-(200)^2}{2(-2000000)}$$

$\Delta x=0.01\;m=1cm$

Answer:

That's a lot of deceleration! The nail would travel 1 cm.