A body starts from rest and moves with a uniform acceleration of 5m/s2 for 5s and then it moves with a constant velocity for 4s. Later it slows down and comes to rest in 5s. Draw the velocity graph for the motion of the body and answer the following questions:
a) What is the maximum velocity attended by the body?
b) What is the distance travelled during this period of acceleration?
c) What is the distance travelled when the body was moving with constant velocity?
d) What is the negative acceleration of the body while slowing down?
e) What is the distance travelled by negative acceleration?
f) What is the total distance travelled?

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2014-08-10T22:22:29+05:30

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See the diagram enclosed. 
At t=0, start at O, origin. Draw a line to A with a slope of 5 for 5 seconds.  For every one second move up by 5 units vertically.
Then draw a horizontal line for 4 seconds reaching D. here t= 9sec.
Now join D with E at t= 9+5 = 14sec on time sline when the body stops ie., velocity is 0. The slope here is found by  height lost / horizontal span  = 25/5 = 5 m/sec²

a)  V at A :  25 m/sec
b) Area enclosed by triangle OAB =  1/2 * 25 * 5 = 62.5 m
c) area of ABCD = 25 * 4 = 100 m
d ) slope = (0-25)/5 = -5 m/sec²
e )  area of triangle DCE = 62.5 m
f ) total area bounded between the OADE and time axis. = 62.5 + 100 + 62.5 = 230m

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