Answer:
Part A) v(t) = u + a t m/sec
Part B) s(t) = s₀ + ut + 0.5 at² meters
Step-by-step explanation:
Given: An object has velocity u m/s at time 0 and constant acceleration a.
<u>Part A) find the velocity after t seconds.</u>
We should know that: ![a = \frac{dv}{dt}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7Bdv%7D%7Bdt%7D)
By integrating both sides with respect to the time t
∴∫ dv = ∫ a dt
∴ v(t) = a t + constant
the object has velocity u m/s at time 0 ⇒ constant = u
<u>∴ v(t) = u + a t </u> m/sec
<u>Part B) find the displacement of the object between time 0 and time t.</u>
We should know that: ![v = \frac{ds}{dt}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bds%7D%7Bdt%7D)
By integrating both sides with respect to the time t
∴∫ ds = ∫ v dt
∵ v(t) = u + a t
∴ ∫ ds = ∫ (u + a t) dt
∴ s(t) = ut + 0.5 at² + constant
Let at t = 0 displacement = s₀ ⇒ ∴ Constant = s₀
<u>∴ s(t) = s₀ + ut + 0.5 at²</u> meters