Question

Based on your equation, what was the car’s approximate initial velocity (at time=0)?


Time (s) Velocity (m/s)
2 13.1
4 19.8
6 28.1
8 34.6

Answer 1

At time t = 0, the initial velocity is approximately 5.9 m/s

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept

Let x represent the time and y represent the velocity.

Using points from the table (2, 13.1) and (8, 34.6). hence:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-13.1=\frac{34.6-13.1}{8-2}(x-2) \\\\y-13.1 = 3.58x -7.2\\\\y = 3.58x+5.9$

Hence at t = 0:

y = 3.58(0) + 5.9 = 5.9

At time t = 0, the initial velocity is approximately 5.9 m/s

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