The position of a body moving along x-axis at time t is given by . . .

Question : The position of a body moving along x-axis at time t is given by x=(t²-4t+6) m. The distance travelled by body in time interval t=0 to t=3 sec is

(1) 5 m

(2) 7 m

(3) 4 m

(4) 3 m

Doubt by Tanishq

Solution :

x=(t²-4t+6) m

Distance travelled by the body at t=0 sec
x₁=(0)²-4(0)+6
x₁=6m

Distance travelled by the body at t=3 sec

x₂=(3)²-4(3)+6
x₂=9-12+6
x₂=15-12
x₂=3 m

x=(t²-4t+6) m

v=dx/dt
v=d(t²-4t+6)/dt
v=2t-4
0=2t-4
-2t=-4
t=-4/-2
t=2 sec

Distance covered by the body at t=2sec
x₃=(2)²-4(2)+6
x₃=4-8+6
x₃=10-8
x₃=2 m

Distance covered
From t=0 to t=2sec
6 m to 2m
=|2-6| = 4 m

Distance covered
From t=2sec to t=3sec
2 m to 3 m
=|3-2| = 1 m

Total Distance Covered
= 4+1

= 5 m

So, (1) 5 m, would be the correct opiton.