Question

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval $t=0tot=5s$ will be.

Answer 1

Step 1: Given Data:

The speed versus time graph is,

Step 2: Formula Used:

According to the second equation of motion,

$S=ut+\frac{1}{2}a{t}^2\dots \dots \dots \dots \dots \dots \dots \left(1\right)$

Where $S=$displacement, $u=$initial speed, $t=$time, and $a=$acceleration.

Step 3: Calculating the distance travelled using equation of motion:

From the figure,

We know that acceleration is defined as the rate of change in velocity.

$a=\frac{8-0}{5-0}=\frac{8}{5}m/s^2$

From the above graph when $t=0,u=0$

Now, substituting the value $t=0$ in equation (1)

$\begin{array}{rcl}S& =& ut+\frac{1}{2}a{t}^2\\ & =& \left(0\right)\left(5\right)+\frac{1}{2}\times \frac{8}{5}\times {\left(5\right)}^2\\ & =& 20m\end{array}$

Step 4: Calculating the distance travelled using speed- time graph:

Distance is the area under the speed-time graph.

From figure area under the speed-time graph is $=\frac{1}{2}\times 5\times 8=20m$

Hence, the distance travelled (in m) by the particle during the time interval $t=0tot=5s$ will be $20m$.