PHYSICS HELP - A particle moves along the x axis..

Question

A particle moves along the x axis according to the equation x = 2.08 + 3.01t − 1.00t²,

 where x is in meters and t is in seconds.

(a) Find the position of the particle at t = 3.40 s.

(b) Find its velocity at t = 3.40 s.

(c) Find its acceleration at t = 3.40 s.

 

Answer 1

Have you taken calculus?

If yes:

a) plug in t=3.4, x is your position x=2.08 + 3.01(3.4) − 1.00(3.4)²

b) take the derivative of x because the rate of change of position is velocity

x=2.08 + 3.01t − 1.00t²

v=3.01-2t plug in t=3.4s v=3.01-2(3.4)

c) take the derivative of v because the rate of change of velocity is acceleration

v=3.01-2t

a=-2

acceleration is constant so it is always -2

if you havent taken Calculus use these two kinematics expressions

x=x₀ + v₀t + 0.5at²

v=v₀+at

Compare x=2.08 + 3.01t − 1.00t² to the first one to get v₀ and a to plug into the second. v₀ is 3.01 and 0.5a=-1 so a=-2

make velocity expression v=3.01-2t

Use x=2.08 + 3.01t − 1.00t² for part a, v=3.01-2t for part b, and since acceleration is constant it has to be -2 for all values of t