Question

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

Answer 1

first we look for whether the particle has changed its direction of motion or not. For that find the time at which v becomes zero.
here
v= 2t- 4
this shows that at t=2s particle comes to rest and has changed its direction of motion.
Now for first 2 seconds
s = 0 + 1/2 (2) 2*2=4m
Now for next one second
S= 1/2 .2. 1*2=1m
So total distance = 4 + 1 = 5m