The velocity graph of a car accelerating from rest to a...

The velocity graph of a car accelerating from rest to a speed of $120 \mathrm{~km} / \mathrm{h}$ over a period of 30 seconds is shown. Estimate the distance traveled during this period.
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Key Concepts

Area Under the Curve

The area under the velocity-time graph is a key concept for finding displacement. By integrating velocity with respect to time, or by calculating the geometric area, one can determine how far an object has traveled over a certain interval.

Unit Conversion

Unit conversion is essential when dealing with physical quantities presented in different units. Often, velocities and time may be given in units that require conversion (such as km/h to m/s) to ensure consistency and accuracy in calculations of distance or displacement.

Velocity-Time Graph

A velocity-time graph displays how an object's velocity changes over time. This type of graph is crucial in kinematics because the area under the curve directly represents the displacement of the object, allowing one to determine the distance traveled during a given period.

Transcript

00:01 For this problem, we are given the velocity graph of a car accelerating from rest to a speed of 120 kilometers per hour over a period of 30 seconds.

00:09 We are asked then to estimate the distance traveled during this period.

00:14 So what i'll do here is just for a rough estimate, we can see that, let's see here, where are the grid lines? we can see that the grid lines are at every five seconds.

00:26 So i'll use that as my first rough estimate, delta t, so delta t equals 5.

00:32 So we can find the lower estimate by first, i'll just write down, delta t times.

00:39 Then i'll take the, we can see that we are increasing over the whole interval.

00:43 So the lower estimate will be taken, will be given by taking the left hand value for each sub rectangle.

00:52 So, or each portion of the remand sum.

00:55 So we can say that it would be about zero plus about 50 for the next, plus the next would be nearly 80.

01:04 So i'll say that that's about 78.

01:06 The next would be at about nearly 100 since let's see.

01:11 Each one of these grid lines vertically is about 20.

01:13 So i'll say that the next will be at about 95.

01:17 Then the next would be about midway between 100 and 120.

01:23 So at 110, i'll say.

01:24 And then lastly, at almost 120, but not quite.

01:29 Not quite...

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