Question

The position of a body moving along $x$-axis at time $t$ is given by $x=\left(t^2-4t+6\right)m$. The distance traveled by the body in time interval $t=0\text{s}$ to $t=3\text{s}$.

• A. $5\text{m}$
• B. $7\text{m}$
• C. $4\text{m}$
• D. $3\text{m}$

Answer 1

The correct option is A

$5\text{m}$

Step 1: Given data

The position of a body moving along $x$-axis.

Time $t$.

$x=t^2-4t+6$

Step 2: To find

Distance traveled by the body in time interval $t=0\text{s}$ to $t=3\text{s}$.

Step 3: Calculate the distance traveled by the body in time intervals $t=0\text{s}$ to $t=3\text{s}$

$x=t^2-4t+6$

The value of distance,

At $t=0\text{s}$, $x_1=6\text{m}$.

At $t=2\text{s}$, $x_2=2^2-(4\times 2)+6=2\text{m}$

So the magnitude of the distance traveled is:

$$\begin{gathered} d_1=6-2 \\ =4\text{m} \end{gathered}$$

Similarly, $t=3\text{s}$, $x_3=3^2-(4\times 3)+6=3\text{m}$

So, the distance traveled from $t=2\text{s}$ to $t=3\text{s}$

$$\begin{gathered} d_2=x_3-x_2 \\ =3-2 \\ =1\text{m} \end{gathered}$$

Thus the total distance is:

$$\begin{gathered} d=d_1+d_2 \\ =4+1 \\ =5\text{m} \end{gathered}$$

Hence, option(A) is correct.