Question

Use the acceleration vs time graph to answer this question. The graph shows the motion with an initial velocity of -4 m/s. Each tick mark on the x-axis represents 1 second. Calculate the velocity at t = 8 seconds.

Answer 1

4 m/s

Step-by-step explanation:

To find the velocity at t = 8 seconds, we will use the following equation:

`v_f=v_i+at`

Where vf is the final velocity, vi is the initial velocity, a is the acceleration and t is the time.

From t = 0 seconds to t = 3 seconds, we have an acceleration of 6 m/s², so we can calculate the velocity at t = 3 seconds as:

`\begin{gathered} v_f=-4m/s+6m/s^2(3\text{ s)} \\ v_f=-4\text{ m/s + 18 m/s} \\ v_f=14\text{ m/s} \end{gathered}`

Now, from t = 3 seconds to t = 8 seconds, the acceleration is equal to -2 m/s². So we need to use the same equation but this time, the initial velocity will be 14 m/s and the time will be 5 seconds because t = 8 s - 3 s = 5s. Then, we get:

`\begin{gathered} v_f=14m/s-2m/s^2(5s) \\ v_f=14\text{ m/s - 10 m/s} \\ v_f=4\text{ m/s} \end{gathered}`

Therefore, the velocity at t = 8 seconds is 4 m/s