Question

The position of a body moving along $x-$ axis at time $t$ is given by $x=(t^2-4t+6)m$. The distance travelled by body in time interval $t=0$ to $t=3$ s is

• A. $5m$
• B. $7m$
• C. $4m$
• D. $3m$

Answer 1

The correct option is A $5m$

The correct option is A.

Given,

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

So, the change in velocity is:

$\frac{dx}{dt}=2t-4$

Since velocity is changing,

At $t=0,x_1=6$

At $t=2,x_2=2$

So the magnitude of the distance traveled is:

$6-2=4m$

At $t=3,x_3=3$

So distance traveled from $t=2s$ to $t=3s$

$x_3-x_2=3-2=1m$

Thus the total distance is:

$4+1=5m$