The graph shows the speed of a remote controlled toy car travelling along a race track. The car's displacement (in metres) can be calculated from the area under this graph. What is it? Give your answer to 3 significant figures.

Question

BlackTom AI · Accepted Answer

The displacement is given by the area beneath the velocity–time graph. To compute it, break the graph into simple shapes whose areas you can calculate directly, then sum them.

First, identify the distinct regions under the curve. In this graph there are three regions:
- A left triangular ramp where velocity increases from 0 to some maximum value at the end of the first segment.
- A middle rectangular (constant velocity) region where velocity is constant at that maximum value for a certain time interval.
- A right triangular ramp where velocity decreases from the maximum value back to 0 at the end.

Next, compute the area of each region:
- Left triangle: Area = (1/2) × base_left × height, where base_left is the time duration of the ramp-up and height is the peak velocity reached at the end of the ramp.
- Middle rectangle: Area = base_mid × height, where base_mid is the duration of the constant-velocity segment and height is the same peak velocity reached during the ramp.
- Right triangle: Area = (1/2) × base_right × height, where base_right is the time duration of the ramp-down and height is again the peak velocity.

Then sum the three areas to obtain the total displacement:
Displacement = Area_left + Area_middle + Area_right = (1/2 × base_left × height) + (base_mid × height) + (1/2 × base_right × height).

If the graph provides numerical values for base_left, base_mid, base_right, and the peak velocity (height), substitute them into the formula to compute the displacement. For example, with height H and total time segments summing to T = base_left + base_mid + base_right, you would compute each term and add them together.

In practice, ensure units are consistent (velocity in m/s, time in s) so that the resulting displacement is in metres. If any dimensions appear in the diagram (e.g., labeled times or velocities), use those values directly. If the graph is scaled or uses rulers, convert the visual measurements to numerical values before applying the area formulas.

Overall, the key idea is: decompose the area under the curve into simple geometric shapes (triangles and rectangle), compute each area with base and height values from the graph, and add them to get the displacement.

The graph shows the speed of a remote controlled toy car travelling along a race track. The car's displacement (in metres) can be calculated from the area under this graph. What is it? Give your answer to 3 significant figures.

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