# How far does the car travel as it brakes? The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied. Use the trapezium rule...

How far does the car travel as it brakes?

The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied. Use the trapezium rule with `m=6` equal intervals.

Here is the graph

http://i50.tinypic.com/2nvr11h.png

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### 1 Answer

The distance travelled `d` by the car is the area under the velocity graph from time `t=0` to time `t=6` seconds.

Using the trapezium rule with `m=6` equal-width intervals` `

`d approx h/2[y_0+y_m + 2(y_1+y_2+y_3+y_4+y_5)]`

where `h` is the interval width (=1) and `m=6`

Therefore, reading approximate values of `y_0,y_1,y_2,y_3,y_4,y_5,y_6` off the graph at `x=0,1,2,3,4,5,6` respectively

`d approx 1/2[52.5 + 0 +2(37.5+26.25+18.75+11.25+3.75)]`

`= 1/2(52.5+195) = 123.75` ft

**The car travels 123.75ft as it brakes**