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A particle is moving with a velocity indicated by v(t)=-t^2+3t, t≥0 ; v[m/s] .?
A: What is the displacement from its initial point to t=4
B: What is the distance travelled in the same period of time
C: When will the displacement be at 0 again ?
1 Answer
- ?Lv 73 years ago
Displacement = ∫ v(t) dt. Here, t = 0 to 4. Compute & answer follows.
Distance: ∫ |v(t)| dt. Here, t = 0 to 4.
Or, figure out where v is >0 and where v is < 0. Do those integrals separately, adding
their magnitudes: ∫ v(t) dt there where v > 0 then + -∫ v(t) dt there where v < 0.
Solve for T in 0 = ∫ v(t) dt, t = 0 to T.
All these are based on knowing how to integrate -t^2+3t.
Show your preliminary steps here if need be!
