Question

4 multiple choice 1 point
in the video around 7:34, the v-t graph is a straight line from (0 s, 0 m/s) to (5 s, 50 m/s). what is the net displacement from 2 s to 4 s?
60 m
40 m
30 m
80 m

Explanation:

Step1: Find acceleration

Acceleration is slope of v-t graph:
$$a = \frac{v_f - v_i}{t_f - t_i} = \frac{50\ \text{m/s} - 0\ \text{m/s}}{5\ \text{s} - 0\ \text{s}} = 10\ \text{m/s}^2$$

Step2: Find velocity at t=2s

Use $v = v_i + at$:
$$v_2 = 0 + (10\ \text{m/s}^2)(2\ \text{s}) = 20\ \text{m/s}$$

Step3: Find velocity at t=4s

Use $v = v_i + at$:
$$v_4 = 0 + (10\ \text{m/s}^2)(4\ \text{s}) = 40\ \text{m/s}$$

Step4: Calculate displacement

Displacement is area under v-t graph (trapezoid area):
$$\Delta x = \frac{1}{2}(v_2 + v_4)(t_4 - t_2) = \frac{1}{2}(20\ \text{m/s} + 40\ \text{m/s})(4\ \text{s} - 2\ \text{s})$$
$$\Delta x = \frac{1}{2}(60\ \text{m/s})(2\ \text{s}) = 60\ \text{m}$$

Answer:

60 m