Speed of a car The accompanying figure shows the...

Speed of a car The accompanying figure shows the time-todistance graph for a sports car accelerating from a standstill. a. Estimate the slopes of secants $P Q_{1}, P Q_{2}, P Q_{3},$ and $P Q_{4}$ arranging them in order in a table like the one in Figure $2.6 .$ What are the appropriate units for these slopes? b. Then estimate the car's speed at time $t=20 \mathrm{~s}$.

Speed of a car The accompanying figure shows the time-todistance graph for a sports car accelerating from a standstill.
a. Estimate the slopes of secants $P Q_{1}, P Q_{2}, P Q_{3},$ and $P Q_{4}$ arranging them in order in a table like the one in Figure $2.6 .$ What are the appropriate units for these slopes?
b. Then estimate the car's speed at time $t=20 \mathrm{~s}$.

Key Concepts

Units of Speed

The appropriate units for speed in these calculations are determined by the units used on the axes of the graph. Typically, if distance is measured in meters and time in seconds, then the units for speed are meters per second (m/s).

Instantaneous Speed

Instantaneous speed refers to the speed of an object at a specific moment in time. It is equivalent to the derivative of the distance with respect to time at that point, and can be estimated by taking the slope of the tangent to the distance-time curve at the desired time.

Distance-Time Graph

A distance-time graph represents how an object's distance from a starting point changes over time. It is used to visually analyze motion, provide insights into the speed and acceleration of an object, and is fundamental for understanding kinematics in physics.

Secant Line

In the context of a distance-time graph, a secant line is a straight line connecting two points on the curve. Its slope represents the average rate of change of distance with respect to time over that interval, essentially reflecting the object's average speed between those two times.

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. On a distance-time graph, it is calculated as the slope of the secant line between two points, providing a measure of how fast an object is moving over a specific time period.

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