Question

FIGURE EX2.9 shows the velocity graph of a particle. Draw the particle’s acceleration graph for the interval $0s\le t\le 4s$

Short answer

The graph of the acceleration of the particle is shown below

Step-by-step solution

Acceleration of a particle.

Acceleration is the slope of the velocity-time graph.

Consider two points on the graph, $\left(t_1,v_1\right)=\left(0,2\right)$and $\left(t_2,v_2\right)=\left(2,2\right)$.

The slope of the velocity-time graph is

$$\begin{gathered} a_x=\frac{v_2-v_1}{t_2-t_1} \\ =\frac{2-2}{2-0} \\ =0\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \end{gathered}$$

Now consider points $\left(t_2,v_2\right)=\left(2,2\right)$and $\left(t_3,v_3\right)=\left(4,4\right)$.

The slope of the velocity-time graph is

$$\begin{gathered} a_x=\frac{v_3-v_2}{t_3-t_2} \\ =\frac{4-2}{4-2} \\ =\frac{2}{2} \\ =1\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \end{gathered}$$

Graph of particle’s acceleration.

From the information obtained in step 1, draw a graph of the acceleration of the particle.

The graph of the acceleration of the particle is shown below.