Question

Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 5.5 mi/h, the time to go one mile decreases by 10 s. What was your original speed?

Answer 1

Let's set up some kinematic equations.

We know velocity is defined as\[v = {d \over t}\]

Your initial velocity can be given as\[v_i = {1 \over t_i}\]and your final velocity can be given as\[v_f = {1 \over t_i - 10}\]

Final velocity can be expressed in terms of initial velocity as\[v_f = v_i + 5.5/3600\]This is expressed in terms of miles per second.
Substituting this into the equation for final velocity\[v_i + 5.5/3600 = {1 \over t_i - 10} \rightarrow v_i = {1 \over t_i - 10} - 5.5/3600\]Solving the equation for initial velocity for time and substituting yields\[v_i = {1 \over (1/ v_i) - 10} - 5.5/3600\]This can be solved for the initial velocity. Remember to multiply the velocity by 3600 to get it back into miles per hour.