A particle moves along the x axis according to the equation x = 50 t + 10 t 2 ,

Question

A particle moves along thexaxis according to the equationx= 50t+ 10t2, wherexis in meters andtis in seconds.

1) Calculate the average velocity of the particle during the first 3.0 s of its motion.

2)Calculate the instantaneous velocity of the particle att= 3.0 s.

3) Calculate the instantaneous acceleration of the particle att= 3.0 s.

4) Using Figure A, in which the blue parabola is the plot ofxversust, indicate how the average velocity during the first 3.0 s can be obtained graphically.

5) Using the graph ofxversust(Figure A) where the blue parabola is the actual plot, indicate how the instantaneous velocity att= 3.0 s can be obtained graphically.

6) From the three lines in Figure B, choose the correct plot ofvversust, and indicate how to find the acceleration att= 3.0 s graphically.

Explanation / Answer

x= 50t + 10t2

so x (t=3) = 240 m

Avg Velocity = 80m/s (Ans 1)

Instantaneous Velocity at time t = x'(t) = 20t + 50

Instantaneous Velocity at 3sec = 110m/s (Ans 2)

Instantaneous Acceleration at any time is 20 m/s2 (Ans 3)

4) Graphically Avg velocity is the slope of red line (fig A)

5) Graphically Instantaneous Velocity is slope of green line (fig A)

6) Graphically The blue line is the velocity graph and its slope is the acceleration (fig B)

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