Question

The following velocity-time graph shows the motion of a cyclist. Find

(i) its acceleration

(ii) its velocity and

(iii) the distance covered by the cyclist in 15 seconds

Answer 1

Step-$1$: The given data

From the graph, we can see that velocity is constant at $20{\mathrm{ms}}^{-1}$

Step-$2$: Calculate the acceleration

Since, $\mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}}$

it is given that velocity is constant.

$$\begin{gathered} \Rightarrow \mathrm{a}=\frac{\mathrm{d}\left(\mathrm{constant}\right)}{\mathrm{dt}} \\ \Rightarrow \mathrm{a}=0 \end{gathered}$$

Hence, acceleration will be $0$

Step-$2$: Calculate velocity

Since velocity is constant given in the graph.

So, velocity will remain $20{\mathrm{ms}}^{-1}$ at each point of time.

Step-$3$: Calculate the distance covered by the cyclist in $15$ seconds

As the acceleration is $0$, so expression for the distance covered will be given as: $\mathrm{s}=\mathrm{v}\times \mathrm{t}$

$\Rightarrow \mathrm{s}=20\times 15=300\mathrm{m}$

Hence, the distance covered will be $300\mathrm{m}$