A particle is moving with the given data. Find the position of the particle. a(t) = t − 4, s(0) = 5, v(0) = 2

Answer 1

Please recall

v(t) = ds/dt

a(t) dv/dt

Given

a(t) = t-4

To find velocity

(t-4) = dv/dt

dv = (t-4)dt

Integrate and apply boundary condition V(0) = 2

V - 2 = t^2-4t

V(t)=t^2-4t+2

Now recall, V(t) = ds/dt

ds = V(t)dt

ds= (t^2-4t+2)dt

Integrate and apply boundary conditions s(0) = 5

s - 5 = t^3/3 - 4t^2/2 + 2t

s = t^3/3-2t^2+2t+5

Answers:

V(t)=t^2-4t+2

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