speed and acceleration of a particle

[mr.burger]

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]

a = dv/dt = 2t^3
Integrate
v = ds/dt = 0.5*(t^4) + v₀

Integrate again
s = .1*t^5 + v₀*t + s₀

Apply given conditions
v(1) = .5(1)^4 + v₀ = 2
v₀ = 1.5
s(2) = 0.1*(2^5) + 1.5*2 + s₀ = 7
s₀ = .8

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

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