Question

the position of a body moving along x axis at time t given by x=(t2- 4t+ 6 )m . the distance travelled by body in time interval t=0 to t=3s is.show with the help of v-t graph =

Answer 1

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Given , x = (t2 - 4t +6) m

v = dx/dt = 2t - 4 m/s

At t = 0 s

v1 = -4 m/s

At t = 3s

v2 = 2 m/s

The velocity time graph is shown above in attachment.

Answer 2

Given,

x=t ²-4t+6

So, the change in velocity is:

dx/dt = 2t-4

Since velocity is changing,

At t= 0,x₁ = 6

At t= 2,x₂ = 2

So the magnitude of the distance traveled is:

6−2=4m

At t= 3,x₃ = 3

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

x₃ - x₂ = 3-2 = 1m

The total distance is:

4+1=5m