Question

An object has velocity u m/s at time 0 and constant acceleration a.

Answer 1

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.

Part A) find the velocity after t seconds.

We should know that: $a = \frac{dv}{dt}$

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

∴ v(t) = u + a t  m/sec

Part B) find the displacement of the object between time 0 and time t.

We should know that: $v = \frac{ds}{dt}$

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

∴ s(t) = s₀ + ut + 0.5 at²  meters