Question

9 the motion of a motor scooter is shown in the graph below. graph: velocity (meters/second) on y - axis, time (seconds) on x - axis, with a line from (0, ~23) to (7, ~2). analyze the graph to determine the acceleration of the motor scooter.
a + 0.33 m/s²
b - 0.33 m/s²
c + 3.0 m/s²
d - 3.0 m/s²

Explanation:

Step1: Recall acceleration formula

Acceleration \( a = \frac{\Delta v}{\Delta t} \), where \( \Delta v = v_f - v_i \) and \( \Delta t = t_f - t_i \).

Step2: Identify initial and final values

From the graph, initial velocity \( v_i = 23 \, \text{m/s} \) (at \( t_i = 0 \, \text{s} \)), final velocity \( v_f = 2 \, \text{m/s} \) (at \( t_f = 7 \, \text{s} \)) (approximate from the graph's scale).

Step3: Calculate \( \Delta v \) and \( \Delta t \)

\( \Delta v = 2 - 23 = -21 \, \text{m/s} \), \( \Delta t = 7 - 0 = 7 \, \text{s} \).

Step4: Compute acceleration

\( a = \frac{-21}{7} = -3.0 \, \text{m/s}^2 \)? Wait, no, maybe my initial velocity was wrong. Wait, looking at the graph, at \( t=0 \), velocity is around 23? Wait, no, the y-axis: let's check the grid. Each major grid is 5 m/s, minor grids: between 0 and 5, maybe 1 m/s per minor? Wait, at t=0, the velocity is 23? Wait, no, maybe I misread. Wait, the first point: at t=0, velocity is 23? Wait, no, the graph starts at (0,23) and goes to (7,2)? Wait, no, maybe the initial velocity is 23? Wait, no, let's recalculate. Wait, maybe the initial velocity is 23 m/s, final at t=7 is 2 m/s? No, that gives -3, but option D is -3, but let's check again. Wait, maybe the initial velocity is 23? Wait, no, maybe the graph is from (0,23) to (7,2)? Wait, no, let's check the axes. The y-axis is velocity (m/s), x-axis time (s). At t=0, the velocity is 23? Wait, no, maybe the first point is (0,23) and at t=7, it's 2? Then \( \Delta v = 2 - 23 = -21 \), \( \Delta t = 7 \), so \( a = -21/7 = -3 \). But wait, the options have D as -3.0 m/s². Wait, but maybe my initial reading is wrong. Wait, maybe the initial velocity is 23? Wait, no, let's check the graph again. Wait, the y-axis: 0,5,10,15,20,25. So at t=0, the velocity is 23 (between 20 and 25, 3 units above 20? Wait, no, each major grid is 5, so 20 to 25 is 5, so each minor grid is 1? So at t=0, it's 23? At t=7, it's 2? Then \( \Delta v = 2 - 23 = -21 \), \( \Delta t = 7 \), so \( a = -21/7 = -3 \). So the answer is D. Wait, but let's check the options. Option D is -3.0 m/s². So that's the calculation.

Answer:

D. \( - 3.0 \, \text{m/s}^2 \)