speed and acceleration of a particle

mr.burger

New member
Joined
Jun 12, 2005
Messages
21
A particle is moving in a straight line. Its acceleration at time t seconds is given by:
a(t)=2t^(3) m/sec^(2)
At time t=1 second, its speed is 2 m/sec
At time t=2 seconds, its position is 7 m

a.)Write its speed equation
b.)Write its position equation
c.)What is its position when its speed is 10 m/sec
 

Gene

Senior Member
Joined
Oct 8, 2003
Messages
1,904
a = dv/dt = 2t^3
Integrate
v = ds/dt = 0.5*(t^4) + v<sub>0</sub>

Integrate again
s = .1*t^5 + v<sub>0</sub>*t + s<sub>0</sub>

Apply given conditions
v(1) = .5(1)^4 + v<sub>0</sub> = 2
v<sub>0</sub> = 1.5
s(2) = 0.1*(2^5) + 1.5*2 + s<sub>0</sub> = 7
s<sub>0</sub> = .8

s = 0.1*t^5 + 1.5*t + 0.8

{s = distance, v = velocity, a = acceleration}
 
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