Question

Comment on the type of motion represented by the displacement-time graphs. What conclusion can we draw from this graph?

Answer 1

1. The position of the body at time $t=0s$ is at $0m$ .
2. This shows that body was initially at rest.
3. The curve from time $t=0s$ to time $t=2s$ is straight line with a positive slope.
4. This shows that the body has a uniform velocity.
5. The slope of the displacement-time graph gives the value of velocity. '
6. Mathematically, the slope of a curve containing points $(x_1,y_1)and(x_2,y_2)$ is given by the equation
   $slope=\frac{y_2-y_1}{x_2-x_1}$
7. Consider the slope of the graph given below.
   
8. From time $t=0s$ to $t=2s$, the slope of the curve is
   $$\begin{gathered} slope=\frac{10-0}{2-0} \\ \Rightarrow slope=5 \end{gathered}$$
9. This means that the body has a uniform velocity of $5m/s$from time $t=0s$ to $t=2s$.
10. At time $t=2s$, the body is at a distance of $10m$.
11. From time $t=2s$ to $t=6s$, the graph is a straight line parallel to x-axis.
12. This means that the slope is zero.
13. So, the velocity is also zero which means the body is at rest.

Thus, the body moves with a constant speed of $5m/s$ for the first $2s$ and covers a distance of $10m$. After that, it stays at rest till the $6^{th}second$.