# Driver going 40km/hr slams on the brakes & goes 3m before stopping - how far for 80?

#### VinnyCee

When the driver applies the brakes of a light truck traveling at $40\,\frac{km}{hr}$, it skids 3 m before stopping. How far will the truck skid if it is traveling $80\,\frac{km}{hr}$ when the brakes are applied?

Here is what I have done, we are supposed to use the work energy formula, but I can't figure out how to relate the small amount of information. There is no mass specified, no kinetic friction coeeficient specified? Please help!

$$V_{i_1}\,=\,40\,\frac{km}{hr}\,=\,11.11\,\frac{m}{s}$$

$$V_{f_1}\,=\,0$$

I figured $t_1$ using kinematics:

$$v_f\,=\,v_i\,+a\,t$$

$$0\,=\,11.1\,+\,a\,t$$

$$s\,=\,s_0\,+\,v_0\,t\,+\,\frac{1}{2}\,a\,t^2$$

$$6\,=\,0\,+\,22.2\,+\,a\,t^2$$

$$t_1\,=\,0.54\,s$$

$$a\,=\,-20.6\,\frac{m}{s^2}$$

Then I use these numbers in another kinematic equation for the 80 km/hr instance:

$$V_f\,=\,V_0\,+\,2\,a\,(s\,-\,s_0)$$

$$0\,=\,22.2\,\frac{m}{s}\,+2\,\left(-20.6\,\frac{m}{s^2}\right)\,(s\,-\,0)$$

$$s\,=\,0.538\,m$$

The answer is actually 12m though.

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#### d_leet

VinnyCee said:
When the driver applies the brakes of a light truck traveling at $40\,\frac{km}{hr}$, it skids 3 m before stopping. How far will the truck skid if it is traveling $80\,\frac{km}{hr}$ when the brakes are applied?

Here is what I have done, we are supposed to use the work energy formula, but I can't figure out how to relate the small amount of information. There is no mass specified, no kinetic friction coeeficient specified? Please help!

$$V_{i_1}\,=\,40\,\frac{km}{hr}\,=\,11.11\,\frac{m}{s}$$

$$V_{f_1}\,=\,0$$

I figured $t_1$ using kinematics:

$$v_f\,=\,v_i\,+a\,t$$

$$0\,=\,11.1\,+\,a\,t$$

$$s\,=\,s_0\,+\,v_0\,t\,+\,\frac{1}{2}\,a\,t^2$$

$$6\,=\,0\,+\,22.2,+\,a\,t^2$$
If the distance it travels before stopping is 3 meters, taking s0 as 0 like you've done then then s should be 3 not 6 since the total displacement is only 3 meters. Also it may have been easier to use a different equation from the start, one that doesn't take into account time since you aren't given a stopping time, such as

vf2 - v02 = 2as

#### VinnyCee

$$v_f^2\,-\,v_0^2\,=\,2\,a\,s$$

$$(0)^2\,-\,\left(22.2\,\frac{m}{s}\right)^2\,=\,2\,\left(-20.6\,\frac{m}{s^2}\right)\,s$$

$$-492.8\,\frac{m^2}{s^2}\,=\,-41.2\,\frac{m}{s^2}$$

$$s\,=\,\frac{-492.8\,\frac{m^2}{s^2}}{-41.2\,\frac{m}{s^2}}\,=\,11.96m$$

That is right if you round up! Thanks for the help.

NOTE: I think we were supposed to solve it using a work-energy formula (i.e. - $\frac{1}{2}\,m\,v_0^2\,+\,\sum\,U\,=\,\frac{1}{2}\,m\,v_f^2$) somehow.

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#### d_leet

VinnyCee said:
$$v_f^2\,-\,v_0^2\,=\,2\,a\,s$$

$$(0)^2\,-\,\left(22.2\,\frac{m}{s}\right)^2\,=\,2\,\left(-20.6\,\frac{m}{s^2}\right)\,s$$

$$-492.8\,\frac{m^2}{s^2}\,=\,-41.2\,\frac{m}{s^2}$$

$$s\,=\,\frac{-492.8\,\frac{m^2}{s^2}}{-41.2\,\frac{m}{s^2}}\,=\,11.96m$$

That is right if you round up! Thanks for the help.

#### arunbg

Note that you don't need to actually find the deceleration to get to the answer. This can be done as follows,
$$v^2 = 2aS=>v^2\varpropto S$$
since acceleration is constant in both cases , we get
$$\frac{{v_1}^2}{{v_2}^2}=\frac{S_1}{S_2}$$
Now you can solve by inserting given values.

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#### VinnyCee

$$\frac{40\frac{km}{hr}}{80\frac{km}{hr}}\,=\,\frac{3\,m}{X}$$

$$X\,=\,6\,m$$

But it's really 12!

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#### Hootenanny

Staff Emeritus
Gold Member
VinnyCee said:
$${\color{red}\frac{40\frac{km}{hr}}{80\frac{km}{hr}}}\,=\,\frac{3\,m}{X}$$

$$X\,=\,6\,m$$

But it's really 12!
You forgot to square the velocities. Re calculate your value and you should obtain 12m.

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