Answer:
1.5 m s⁻²
Step-by-step explanation:
The provided graph is a velocity-time graph illustrating how an object's velocity changes over time.
The slope of the line on a velocity-time graph represents the object's acceleration.
- A positive slope indicates positive acceleration (speeding up in the positive direction).
- A negative slope indicates negative acceleration (slowing down or speeding up in the negative direction, also called deceleration).
- A zero slope (a horizontal line) indicates constant velocity (no acceleration).
The magnitude of acceleration at a specific time t on a velocity-time graph is the absolute value of the slope of the graph at that moment. This slope represents the change in velocity (Δv) divided by the change in time(Δt). Since the magnitude of acceleration focuses on the size of this change regardless of direction, it is calculated as the absolute value of the change in velocity divided by the change in time:
[tex]|\mathbf{a}|=\left|\dfrac{\Delta v}{\Delta t}\right|[/tex]
From observation of the given graph, the velocity decreases linearly from 3 m s⁻¹ at t = 4 seconds to 0 m s⁻¹ at t = 6 seconds. Therefore, the magnitude of acceleration at t = 5 seconds can be determined by finding the absolute rate of change of velocity within that time interval.
[tex]|\mathbf{a}|=\left|\dfrac{v_2-v_1}{t_2-t_1}\right|\\\\\\|\mathbf{a}|=\left|\dfrac{0-3}{6-4}\right|\\\\\\|\mathbf{a}|=\left|-\dfrac{3}{2}\right|\\\\\\|\mathbf{a}|=1.5\; \sf m\;s^{-2}[/tex]
Therefore, the magnitude of acceleration at t = 5 seconds is:
[tex]\LARGE\boxed{\boxed{\sf 1.5 \; m\; s^{-2}}}[/tex]
