+0  
 
0
340
1
avatar

Suppose that we have an object that moves into a Δx path. Its speed doubles as a period of Δt passes. No matter the distance of the path, find a way to express the time that it will take the object to go from xstart  to xfinish with Δx and Δt being variables 

Guest Jun 22, 2017
 #1
avatar+169 
+2

\(\text{We know that the velocity doubles every interval }\Delta t\text{, hence the velocity}\\ \text{must adhere to the general formula: }v(t)=v_0\cdot2^{t/\Delta t}\text{, with }v_0\text{ the initial}\\ \text{velocity. The distance travelled is of course the integral of the velocity}\\\text{over the time spent travelling:}\\ \Delta x=\int^{t_e}_0v(t)\text{d}t=v_0\int^{t_e}_02^{t/\Delta t}\text{d} t=\frac{v_o\Delta t}{\ln 2}(2^{t_e/\Delta t}-1).\\ \text{We require the time it takes to travel this distance }(t_e)\text{ so we rewrite the}\\ \text{formula to extract }t_e:\\ t_e=\frac{\Delta t}{\ln 2}\ln\left(\frac{\Delta x\ln 2}{v_0\Delta t}+1\right).\\ \text{In order to test our answer we try }\Delta x=0\text{ this should give us }t_e=0,\\ \text{and indeed it does.}\)

Honga  Jun 23, 2017

12 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.