The position of a body moving along x axis at time t is given by x=(t^2 -4t + 6)m

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1

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=3s is____.

2

The following steps are to be followed while solving the query:

  1. Using the distance relation find the velocity relation. v = dx/dt = 2t - 4
  2. Now, find the speed at points t = 0 and t = 3 s and then plot a graph of the same. V (t=0) = -4 m/s and v (t=3) = 2 m/s
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  3. Find the area under the curve for this time interval and you will get the distance. The area is shown in shaded blue colour. You will get s = 4 + 1 = 5 m