sph3u1 - unit 1 kinematics\n13. convert the following position - time graph into a velocity time graph, and…

sph3u1 - unit 1 kinematics\n13. convert the following position - time graph into a velocity time graph, and an acceleration time graph.\n4 marks - c\nkinematic equations:\n$deltavec{d}=\frac{vec{v}_i+vec{v}_f}{2}cdotdelta t$\n$vec{v}_f=vec{v}_i+vec{a}delta t$\n$deltavec{d}=vec{v}_idelta t+\frac{1}{2}vec{a}delta t^2$\n$deltavec{d}=vec{v}_fdelta t-\frac{1}{2}vec{a}delta t^2$\nother useful equations:\n$d = vdelta t$\n$vec{v}_{avg}=\frac{deltavec{d}}{delta t}$\n$vec{a}=\frac{deltavec{v}}{delta t}$\n$m=\frac{rise}{run}=\frac{y_2 - y_1}{x_2 - x_1}$

sph3u1 - unit 1 kinematics\n13. convert the following position - time graph into a velocity time graph, and an acceleration time graph.\n4 marks - c\nkinematic equations:\n$deltavec{d}=\frac{vec{v}_i+vec{v}_f}{2}cdotdelta t$\n$vec{v}_f=vec{v}_i+vec{a}delta t$\n$deltavec{d}=vec{v}_idelta t+\frac{1}{2}vec{a}delta t^2$\n$deltavec{d}=vec{v}_fdelta t-\frac{1}{2}vec{a}delta t^2$\nother useful equations:\n$d = vdelta t$\n$vec{v}_{avg}=\frac{deltavec{d}}{delta t}$\n$vec{a}=\frac{deltavec{v}}{delta t}$\n$m=\frac{rise}{run}=\frac{y_2 - y_1}{x_2 - x_1}$

Answer

Explanation:

Step1: Recall the relationship between position - velocity

Velocity is the slope of the position - time graph. When the position - time graph is increasing, the velocity is positive; when it is decreasing, the velocity is negative; and when it is flat (horizontal), the velocity is zero.

Step2: Analyze the position - time graph segments

At the start, the position - time graph is increasing with a positive slope, so the velocity is positive. As it reaches the peak and becomes flat, the velocity drops to zero. Then as it starts to decrease, the velocity becomes negative.

Step3: Recall the relationship between velocity - acceleration

Acceleration is the slope of the velocity - time graph. When the velocity is increasing (getting more positive or less negative), the acceleration is positive. When the velocity is decreasing (getting less positive or more negative), the acceleration is negative. When the velocity is constant, the acceleration is zero.

Step4: Analyze the velocity - time graph for acceleration

When the velocity is changing from positive to zero (as the position - time graph levels off), the acceleration is negative. When the velocity is changing from zero to negative (as the position - time graph starts to decline), the acceleration is negative. When the velocity is constant (flat sections in the idealized velocity - time graph), the acceleration is zero.

For actually drawing the graphs:

  • On the velocity - time graph: Start with a positive non - zero value as the position - time graph is initially rising. It then drops to zero as the position - time graph levels off, and then becomes negative as the position - time graph falls.
  • On the acceleration - time graph: It will have negative values when the velocity is changing (either from positive to zero or from zero to negative), and zero values when the velocity is constant (at the peak of the position - time graph and other possible flat sections in the velocity graph).

Since this is a qualitative conversion of graphs and no specific numerical values are given, we focus on the general shape and trends.

Answer:

The velocity - time graph will start with a positive value, decrease to zero at the peak of the position - time graph, and then become negative as the position - time graph falls. The acceleration - time graph will have negative values when the velocity is changing and zero values when the velocity is constant.