Variable acceleration?

The velocity v ms-1 of a particle after t seconds is given by v=t−3t2
The initial displacement of the particle from the origin is 3m.

The displacement of the particle from the origin after 5 seconds is ____m

2 Answers
Douglas K.
Apr 19, 2018

x = -219/2" m"

Explanation:

We know that v = dx/dt:

dx/dt = t-3t^2

where x is the displacement

Integrating:

x = int t -3t^2 dt

x = t^2/2-t^2+x_0

We are told that x_0 = 3" m"

x = t^2/2-t^3+3" m"

Evaluate at t = 5" s"

x = 5^2/2-5^3+3" m"

x = -219/2" m"

Shiva Prakash M V
Apr 19, 2018

the displacement of the particle after 5 seconds is
s=-109.5

Explanation:

v=t-3t^2
v=(ds)/(dt)

(ds)/(dt)=t-3t^2

ds=(t-3t^2)dt
intds=int(t-3t^2)dt

s=s_0+1/2t^2-t^3

s=3,t=0

3=s_0+1/2(0)^2-(0)^3

s_0=3

s=3+1/2t^2-t^3

Substitute t=5sec

s=3+1/2(5)^2-(5)^3

s=3+25/2-125

s=3+12.5-125

s=15.5-125

s=-109.5
Hence, the displacement of the particle after 5 seconds is
s=-109.5

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