Derive the described kinematic equations using the information given. Starting w

Question

Derive the described kinematic equations using the information given. Starting with the Master Kinematic Equation, derive the velocity of an object moving with constant acceleration. Now, starting with the relationship, a = dv/dt, once again derive the velocity of an object moving with constant acceleration. Starting with the relationship, v = dx/dt, derive the Master Kinematic Equation for an object moving with constant acceleration. Derive the following kinematic equation using your knowledge of the other kinematic equations. v^2 = v_0^2 + 2a(x - x_0) An airplane pilot wishes to fly due south. A wind of 25 km/h is blowing toward the west. If the flying speed of the plane is 300.0 km/h (its speed in still air), in what direction should the pilot head?

Explanation / Answer

Let;'s start with equation for acceleration of a body,

x = x0 + ut + 1/2 at^2---eq)(1)

a) Using equation 1,

( x - x0) = ut + 1/2 at^2

differentiating the equation,

dx = ( u + at) dt

but dx/dt = v

v = u =at

b) a= dv/dt

adt = dv

dv = adt

integerating on both sides,

( v -u ) = at

v = u+ at

c) v = dx/dt

vdt = dx

dx = vdt

dx = ( u+at)dt

integerating ,

( x - x0) = ut + 1/2 at^2

x = x0 + ut + 1/2 at^2

d) a= dv/dt

a= dv (dx) / dx (dt)

a= dv v / dx

adx= vdv

integertaing on both sides,

a ( x - x0) = v^2/ 2- v0^2/2

2a ( x-x0) = v^2- v0^2

v^2 = v0^2 + 2a (x-x0)

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.