Question is: a car travelling at 140 km/h decelerates for 20 secs. During this time it travels 500 m. What is its deceleration? What is its speed...

Sunday, February 21, 2010

Question is: a car travelling at 140 km/h decelerates for 20 secs. During this time it travels 500 m. What is its deceleration? What is its speed...

Hello!

As I understand, the deceleration is uniform (the same all the time). Denote it as $\displaystyle{a}\gt{0}$ and denote the initial speed as $\displaystyle{V}_{{0}}.$ In m/s $\displaystyle{V}_{{0}}=\frac{{140}}{{3.6}}.$

Then the speed is $\displaystyle{V}{\left({t}\right)}={V}_{{0}}-{a}\cdot{t}$ (note the minus sign), and the displacement is $\displaystyle{D}{\left({t}\right)}={V}_{{0}}{t}-\frac{{{a}{{t}}^{{2}}}}{{2}}.$

It is given that $\displaystyle{D}{\left({20}\right)}={500},$ therefore $\displaystyle{V}_{{0}}\cdot{20}-\frac{{{a}\cdot{{20}}^{{2}}}}{{2}}={500}.$ From this we find $\displaystyle{a}={2}\cdot\frac{{\frac{{140}}{{3.6}}\cdot{20}-{500}}}{{{20}}^{{2}}}\approx{1.39}{\left(\frac{{m}}{{{s}}^{{2}}}\right)}.$

Then we can find the speed after deceleration: it is

$\displaystyle{V}{\left({20}\right)}={V}_{{0}}-{a}\cdot{20}\approx\frac{{140}}{{3.6}}-{20}\cdot{1.39}\approx{11.1}{\left(\frac{{m}}{{s}}\right)}.$

The value is positive which means the direction of movement remains the same.

The answers: the deceleration is about $\displaystyle{1.39}\frac{{m}}{{{s}}^{{2}}},$ and the final speed is about $\displaystyle{11.1}\frac{{m}}{{s}}.$

Ninenotes

Sunday, February 21, 2010

Question is: a car travelling at 140 km/h decelerates for 20 secs. During this time it travels 500 m. What is its deceleration? What is its speed...

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