A ball is thrown up vertically and returns back to the thrower in 6 sec. assuming that there is no air friction plot velocity time graph. From the graph calculate (i) deceleration (ii) acceleration (iii) Total distance covered by stone (iv) Average velocity

Asked by Rajiv | 22nd May, 2015, 08:17: PM

Expert Answer:

The velocity time graph for the first six seconds is given below:
 
 
(i) Deceleration is given as the slope of the graph for the first 3 seconds.
 
begin mathsize 14px style deceleration space straight a equals slope equals fraction numerator 0 minus 30 over denominator 3 minus 0 end fraction equals fraction numerator negative 30 over denominator 3 end fraction equals negative 10 space straight m divided by straight s squared end style
 
(ii) Acceleration is given as the slope of the graph for the last 3 seconds.
 
begin mathsize 14px style Acceleration space straight a equals slope equals fraction numerator 30 minus 0 over denominator 6 minus 3 end fraction equals 30 over 3 equals 10 space straight m divided by straight s squared end style
 
(iii) Total distance covered is given as the area under the curve.
 
begin mathsize 14px style straight d equals area equals 1 half cross times 3 cross times 30 plus 1 half cross times 3 cross times 30 equals 3 cross times 30 equals 90 space straight m end style
 
(iv) Average velocity is given as 
 
begin mathsize 14px style straight v subscript av equals fraction numerator Total space displacement over denominator Total space time end fraction equals 0 as space displacement space is space zero space since space the space ball space comes space back space to space th space thrower. end style

Answered by Romal Bhansali | 24th May, 2015, 06:25: PM

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