A particle starts from rest and moves with a uniform acceleration of 5m/s2 for 10s 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 calculate the total distance travelled ?
Answers
Answer:
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 5
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
