(b)Given the shown v-t diagram (1) construct a-t and s-t diagram (11) Using diagrams, find total distance travelled through the first (35 s). V m mis time s 25s (V4 dingram 6 m/s
For the given velocity time graph
From t = 0 to t = 5 s
velocity u = 3m/s
Acceleration a = 0 {Velocity is constant}
and the distance traveled
s = v*t = 3 m/s*5 s
= 15 m
From t = 5 to t = 15 s
velocity changes from u = 3m/s to u' = -6 m/s
Acceleration a:
by the equation of motion
u' = u+at
-6 m/s = 3 m/s +a (10 s) (Position curve will be decreasing its slope)
a = -0.9 m/s2
and the distance traveled will be given by the third equation of motion:
So the position of the particle at t = 15 sec will be
s(t =15) = 15 m -25 m
= -10 m
From t = 15 to t = 25 s
velocity changes from u' = -6 m/s to v = 5 m/s
Acceleration a:
by the equation of motion
v = u'+at
5 m/s = -6 m/s +a'(10 s)
a = 1.1 m/s2
and the distance traveled will be given by the third equation of motion:
(Position curve will be increasing its slope)
So the position of the particle at t = 25 sec will be
s(t = 25) = -10 m +27.72 m
= 17.72 m
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