Question

Calculate v0 at t0, v2 at t2, and v4 at t4 by drawing tangent lines to the curve x(t).

Answer 1

To calculate the initial and subsequent velocities at given times from a position vs. time graph, draw tangent lines to the curve at these times and calculate the slope of each tangent line.

Step-by-step explanation:

The student's question revolves around finding the initial velocity (v0) at time zero (t0), the velocity at time two seconds (v2) at t2, and the velocity at time four seconds (v4) at t4 using the slope of tangent lines to a position vs. time (x(t)) graph. The concept behind this calculation is based on the formula x = xo + vt, where x is the final position, xo is the initial position, v is the constant velocity, and t is the time elapsed. To calculate the velocities v0, v2, and v4, one would draw tangent lines to the curve at the respective times and use the slope formula (slope = rise/run) to find the instantaneous velocities. The slope represents the velocity at that point on the graph.

To calculate v0, v2, and v4:

1. Determine the points where the tangent touches the curve at times t0, t2, and t4.
2. Draw the tangent lines at these points and find two points on each tangent line to calculate the slope.
3. Use the slope formula with your determined points on each tangent to calculate v0, v2, and v4 as the slope of these tangent lines gives the instantaneous velocity.