## Related questions with answers

When you drive behind another car, what is the minimum distance you should keep between the cars to avoid a rear-end collision if the other car were to suddenly stop (it hits, say, a stationary truck)? Some drivers use a " $2$ second rule" while others use a "$3$ second rule." To apply such rules, pick out an object such as a tree alongside the road. When the front car passes it, begin to count off seconds. For the first rule, you want to pass that object at a count of $2 \mathrm{~s}$, and for the second rule, $3 \mathrm{~s}$. For the $2 \mathrm{~s}$ rule, what is the resulting car-car separation at a speed of $(a)$ $15.6 \mathrm{~m} / \mathrm{s}$ ($35 \mathrm{~m} / \mathrm{s}$), slow and $(b)$ $31.3 \mathrm{~m} / \mathrm{s}$ $(70 \mathrm{mi} / \mathrm{h}$), fast? For the $3 \mathrm{~s}$ rule, what is the car-car separation at a speed of $(c)$ $15.6 \mathrm{~m} / \mathrm{s}$ and $(d)$ $31.3 \mathrm{~m} / \mathrm{s}$ ? To check if the results give safe trailing distances, find the stopping distance required of you at those initial speeds. Assume that your car's braking acceleration is $-8.50 \mathrm{~m} / \mathrm{s}^2$ and your reaction time to apply the brake upon seeing the danger is $0.750 \mathrm{~s}$. What is your stopping distance at a speed of $(e)$ $15.6 \mathrm{~m} / \mathrm{s}$ and $(f)$ $31.3 \mathrm{~m} / \mathrm{s}$ ? $(g)$ For which is the $2 \mathrm{~s}$ rule adequate? $(h)$ For which is the $3 \mathrm{~s}$ rule adequate ?

Solution

Verified**Givens**

- $v_1=15.6\ \frac{\text{m}}{\text{s}}$ - the slower speed
- $v_2=31.3\ \frac{\text{m}}{\text{s}}$ - the faster speed
- $\tau_1=2\ \text{s}$ - the two second rule
- $\tau_2=3\ \text{s}$ - the three second rule
- $a=8.5\ \frac{\text{m}}{\text{s}^2}$ - the deceleration
- $\Delta t=0.75\ \text{s}$ - the reaction time

**Required**

- determine which of the rules is appropriate in which situation

*How can we use the known expressions for the speed and the distance travelled by the car in order to solve this problem?*

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