Question

Part A At t tt = 2.0 s s , what is the particle's position? Express your answer to two significant figures and include the appropriate units. x x = nothing nothing SubmitRequest Answer Part B At t tt = 2.0 s s , what is the particle's velocity? Express your answer to two significant figures and include the appropriate units. v x vx = nothing nothing SubmitRequest Answer Part C At t tt = 2.0 s s , what is the particle's acceleration? Express your answer to two significant figures and include the appropriate units. a x ax = nothing nothing

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The particle's position is  $x_{2} = 10 m$

The particle's velocity is  $v = 2 \ m/s$

Explanation:

From the question we are told that  

       $x = 2m$  at  $t_o = 0 \ sec$

        and  from the graph at t = 0  $v = 6 /m$

Now the acceleration which is the slope of the graph is mathematically represented as

        $a = - \frac{6 - 4}{3-2}$

        $a = - 2 m/s^2$

The negative sign shows that it is a negative slope

       Now to obtain the velocity at t = 2 sec

We use the equation of motion as follows

          $v = v_o + at$

  substituting values '

       $v = 6 + (-2)(2)$

      $v = 2 \ m/s$

Now to obtain the position of the particle at   v = 2 m/s

      We use the equation of motion as follows

       $v^2 = v_o ^2 + 2 ax$

So    $2 ^2 = 6^2 + 2(-2)x$

       $4x = 32$

       $x = 8 m$

From above    $x = 2m$  at  $t_o = 0 \ sec$

So the position at t =  2 s

           $x_{2} = x + x_o$

          $x_{2} = 2 + 8$

        $x_{2} = 10 m$