Questions: which diagram shows the equation v=2t+4 v (m/s) 6 5 4 3 2 1 0 0 1 2 t (s) v (m/s) 10 9 8 7 6 5 4 3 2 1 0 0 1 2 t (s)

which diagram shows the equation v=2t+4 v (m/s) 6 5 4 3 2 1 0 0 1 2 t (s) v (m/s) 10 9 8 7 6 5 4 3 2 1 0 0 1 2 t (s)
Transcript text: which diagram shows the equation v=2t+4 v (m/s) 6 5 4 3 2 1 0 0 1 2 t (s) v (m/s) 10 9 8 7 6 5 4 3 2 1 0 0 1 2 t (s)
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Solution

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Solution Steps

Step 1: Analyze the first graph

The first graph shows a velocity that starts at 4 m/s and decreases linearly to 0 m/s over 2 seconds. This indicates constant negative acceleration (deceleration).

Step 2: Calculate the acceleration for the first graph

The acceleration is the change in velocity divided by the change in time:

\(a = \frac{v_f - v_i}{t_f - t_i} = \frac{0 - 4}{2 - 0} = \frac{-4}{2} = -2 \, m/s^2\)

Step 3: Analyze the second graph

The second graph shows a velocity that starts at 2 m/s and increases linearly to 8 m/s over 3 seconds. This indicates a constant positive acceleration.

Step 4: Calculate the acceleration for the second graph

The acceleration is the change in velocity divided by the change in time:

\(a = \frac{v_f - v_i}{t_f - t_i} = \frac{8 - 2}{3 - 0} = \frac{6}{3} = 2 \, m/s^2\)

Final Answer

First graph: \( \boxed{-2 \, m/s^2} \) Second graph: \(\boxed{2 \, m/s^2} \)

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