#### To determine

**To estimate:**

The distance traveled

#### Answer

*0.725kms*

#### Explanation

**1) Concept:**

Area under the graph is

*A=limn→∞∑i=1nfxi∆x*

where,

*∆x=b-an & xi=a+i∆x*

2) **Calculation:**

The velocity graph of the car accelerating from rest to a speed of

*120kmh *

over a period of *30* seconds.

So, the interval *0, 30* with *n=6*.

Find out * ∆x*.

*∆x=b-an=30-06=5*

For an increasing function, using left end points gives an underestimate and using right end points gives an overestimate. Therefore, use the mid-point.

*M6=∑i=05fxi'∆x*

*=531.25+66+88+103.5+113.75+119.25*

*=2608.75*

But from the graph, there is *x-axis* measured in seconds and *y-axis* measured in km/h.

So to convert the km/h into the km/s.

There are *3600* seconds in an hour

Traveled distance is

*=2608.75×13600*

*=0.725kms*

**Conclusion:**

The traveled distance is

*0.725kms*