  ToughSTEM  ToughSTEM
A question answer community on a mission
to share Solutions for all STEM major Problems.
Cant find a problem on ToughSTEM?
1
The acceleration of a bus is given by ax(t)=αt, where α = 1.28m/s3 is a constant. Part A If the bus's velocity at time t1 = 1.13s is 5.09m/s , what is its velocity at time t2 = 2.02s ? If the bus's position at time t1 = 1.13s is 5.92m , what is its position at time t2 = 2.02s ?  Edit
Added Fri, 04 Sep '15 Community
1
Comment  Solutions
0

a?(t) = Î±t

Î± = 1.28m/sï¿½ = accel.

dv/dt = a?(t) =at or dv = atdt

dv =  ?tdt => v = at2 / 2 + C

also bus's velocity at time t1 = 1.13s is 4.96m/s

=> 4.96 = a1.13ï¿½ / 2 + C = 1.28(1.2769) / 2 + C = 0.817216 + C

=> C = 4.96 - 0.817216 = 4.142784 m/s

therefore v = at2 / 2 + 4.142784

at t = 2.02 => v = 1.28(2.02)2/2 + 4.142784 = 6.75424 m/s

ii) v = ds/dt = at2 / 2 + 4.142784

similarly integrating => s = ?tï¿½ / 6 + 4.142784t + D

bus's position at time t1 = 1.13s is 5.92m

=> 5.92 = 1.28(1.13)3 / 6 + 4.142784(1.13) + D

or 5.92 = 4.98882+ D or D = 0.931175 m

therefore s = at3 / 6 + 4.142784t + 0.931175

at t = 2.02 s => s = 1.28(2.02)3 / 6 + 4.142784(2.02) + 0.931175

= 11.05797868 ~= 11.0579 m  Edit
Added Fri, 04 Sep '15 Community
1
Comment  Close Choose An Image
or
Get image from URL
GO
Close Back
Close
What URL would you like to link?
GO             α
β
γ
δ
ϵ
ε
η
ϑ
λ
μ
π
ρ
σ
τ
φ
ψ
ω
Γ
Δ
Θ
Λ
Π
Σ
Φ
Ω
Copied to Clipboard

to interact with the community. (That's part of how we ensure only good content gets on ToughSTEM)
OR      OR
ToughSTEM is completely free, and its staying that way. Students pay way too much already.
Almost done! Welcome to the Club!
Choose a new Display Name
Only letters, numbers, spaces, dashes, and underscores, are allowed. Can not be blank.
Great! You're all set, . A question answer community on a mission
to share Solutions for all STEM major Problems.
Why
The Purpose
How
The Community
Give Feedback Tell us suggestions, ideas, and any bugs you find. Help make ToughSTEM even better.