The velocity graph of a particle moving along the x-axis. Its initial position i

Question

The velocity graph of a particle moving along the x-axis. Its initial position is X_0 = 2.0 m at t_0 = 0 s. At t = 1.0 s, what is the particle's position? Express your answer to two significant figures and include the appropriate units. x = At t = 1.0 s, what is the particle's velocity? Express your answer to two significant figures and include the appropriate units. v_x = At t = 1.0 s, what is the particle's acceleration? Express your answer to two significant figures and include the appropriate units. a_x =

Explanation / Answer

v = 2t

Since , v = dx/dt

dx/dt = 2t

dx = 2tdt

Integrating both sides

x = t^2 + c where c is a constant .

At t = 0 , you're given x0 = 2 , i.e , c = 2.

So , x = t^2 + 2 .

At t = 1, x = 1 + 2 = 3 m ............a)

From the graph , at t = 1 , v = 2 m/s . ..........b)

And acceleration a = dv/dt = 2 m/s^2 (since v = 2t) ..........c)

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