Question

A particle starts from rest and moves with a uniform acceleration of 5 m/s² for 10 s and
then it moves with a constant velocity for 4 s. Later it slows down and comes to rest in 5
s. Draw the velocity graph for the motion of the body and calculate the total distance
travelled?
pls its urgent

Answer 1

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 O. 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

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