Question

questions 11 - 12. the object shown in the position - time graph above: (a) started off slowly, sped up, and then slowed down again. (b) started off rapidly, slowed down, and then sped up again. (c) has a constant positive acceleration. (d) has a constant negative acceleration. (e) both (b) and (d). the magnitude of the acceleration of the object is about (a) 0.56 m/s/s (b) 1.2 m/s/s (c) 3 m/s/s (d) 9.8 m/s/s (e) cannot be determined

Explanation:

Step1: Analyze velocity from position - time graph

The slope of a position - time graph gives velocity. Initially, the slope is large (steep), so the velocity is high. As time progresses, the slope decreases (graph becomes less steep), so the velocity decreases. Then the slope starts increasing again (graph gets steeper), so the velocity increases again.

Step2: Analyze acceleration from velocity - time relationship

Acceleration is the rate of change of velocity. Since velocity first decreases and then increases, the acceleration is not constant.

Step3: For magnitude of acceleration

We can estimate the acceleration using the kinematic equation \(a=\frac{\Delta v}{\Delta t}\). However, without exact values of velocity at different times (which we can't precisely get from the graph without more information), we cannot accurately calculate the acceleration.

Answer:

1. B. started off rapidly, slowed down, and then sped up again.
2. E. cannot be determined