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. 5 m
• B. 7 m
• C. 4 m
• D. 3 m

Answer 1

The correct option is A 5 m

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,

$Att=0,x_1=6$

$Att=2,x_2=2$

So the magnitude of the distance traveled is:

$6-2=4m$

$Att=3,x_3=3$

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

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

Thus the total distance is:

$4+1=5m$