Can you find the speed at 3s. The answer is 29.3 try drawing tangent and finding the answer and explain it to me. I got 30m/s---**Question Stem:**
A car accelerates from rest as shown on the graph shown below.
**Chart Description:**
* **Type:** Line chart / Position-Time Graph
* **Title:** distance (m) vs. time (s)
* **X-axis:** Labeled "time (s)". Scale ranges from 0 to 3.5 seconds, with major tick marks at 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5. The grid lines are spaced at 0.1 second intervals.
* **Y-axis:** Labeled "distance (m)". Scale ranges from 0 to 60 meters, with major tick marks at 0, 10, 20, 30, 40, 50, 60. The grid lines are spaced at 2 meter intervals.
* **Data Series:** A single blue line representing the distance traveled by the car as a function of time.
* **Curve Shape:** The line starts at the origin (0,0) and is curved upwards, appearing parabolic, indicating increasing velocity (acceleration).
* **Approximate Data Points:**
* (0 s, 0 m)
* (1 s, ~5 m)
* (2 s, ~20 m)
* (3 s, ~45 m)
* (3.5 s, ~60 m)
* **Grid:** A grid is present, aligned with the tick marks on both axes.
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We have a position-time graph showing a car's motion. The curve is parabolic, indicating constant acceleration from rest. To find the instantaneous speed at t equals 3 seconds, we need to find the slope of the tangent line at that point.
Now we draw the tangent line at t equals 3 seconds. The tangent line just touches the curve at this point and represents the instantaneous rate of change. We select two points on this tangent line: point A at 2.0 seconds, 15.4 meters, and point B at 4.0 seconds, 74.0 meters.