a body at rest is given an initial uniform acceleration of 8.0m/s for 30s after which the acceleration is reduced to 5.0m/s for the next 20s.the body maintains the speed attained for 60s after which is brought to rest in 20s.draw the velocity time graph of the motion using the information above
Answers
A body, at rest, is given an initial acceleration of 8 m/s 2 for 30 s after which the acceleration is reduced to 5 m/s 2 for the next 20 s. The body maintains the speed attained for 60 s after which it is brought to rest in 20 s. We want to plot the v-t graph.
v= u+at, where v, u, a and t are the final velocity, initial velocity, acceleration and time, respectively.
For t = 0s to t =30s ,a = 8 m/s²
For t=30 s to t=50 s ,a=5 m/s².
For t=50 s to t=110 s ,a=0 m/s².
For t = 110s to t = 130s ,a is such that the body comes to rest at the end of this period.
⇒ For t = 0s to t = 30s ,v = 0+8t ⇒ v = 8t m/s.
⇒ At t = 30s, v = 8×30 = 240 m/s.
⇒ For t = 30 s to t = 50 s ,v=240+5(t−30) ⇒ v = 90+5t m/s.
⇒ At t = 50s, v = 90+5×50 = 340 m/s.
⇒ For t = 50s to t = 110s ,v = 340 m/s.
⇒ For t = 110 s to t = 130s ,v = 340+a(t−110).
The body comes to a halt at t = 130s ⇒ 0 = 340+a(130−110).
⇒ 0 = 340+20a ⇒ a= −34020 = −17 m/s 2.
⇒ For t = 110s to t = 130s ,v = 340−17(t−110) = 2210−17t m/s.
The velocity-time graph is given below.
Hope this helps you.
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