Question

In Problem 79, you are given the kinematic equation or

equations that are used to solve a problem. For each of these, you are to:

a. Write a realistic problem for which this is the correct equation(s).

Be sure that the answer your problem requests is consistent with

the equation(s) given.

b. Draw the pictorial representation for your problem.

c. Finish the solution of the problem.

$x_1=0m+0m/s^2(5s-0s)+\frac{1}{2}(20m/s^2){(5s-0s)}^2$

$x_2=x_1+v_{1x}(10s-5s)$

Short answer

The kinematic equation of motion of an object at constant acceleration is given by:

$$\begin{gathered} v_{fs}=v_{is}+a_s\Delta t \\ {s}_f=s_i+v_s\Delta t+\frac{1}{2}{a}_s\left(\Delta t\right) \\ {v_{fs}}^2={v_{is}}^2+2a_s\Delta s \end{gathered}$$

Step-by-step solution

The realistic problem to represent the given equations:

Consider a battleship fires a missile from rest. The missile accelerates uniformly at 20m/s² for 5 s till it reaches its maximum peak velocity. It maintains the peak velocity. What is the distance that the missile has travelled after 10 s?

Pictorial presentation of the given equations:

Solving the given equations:

Solve the equation for v_1x:

$$\begin{gathered} v_{1x}=0+20(5-0) \\ =100m/s \end{gathered}$$

Solve the equation for x₁:

$x_1=0+0(5-0)+\frac{1}{2}\times 20\times {(5-0)}^2=250m$

Solve the equation for x₂:

$$\begin{gathered} x_2=250+100\left(10-5\right) \\ =750m \end{gathered}$$