Question

A particle is moving along the x-axis. Its acceleration is given by 𝑎𝑥 = 𝑐𝑡 − 𝑑𝑡²

with c=2.0m/s³and d=0.24m/s⁴.The particle is at rest at the origin at t=0. Find position and 

velocity as functions of time. What is the maximum velocity the particle reaches?

Answer 1

$$v=\int(ct-dt^2)\text dt=t^2-0.08t^3.\\ v_\text{ max}=23.1\text{ m/s}.\\ x=\int(t^2-0.08t^3)\text dt=\frac{t^3}3-0.02t^4.$$