Question

particle’s position along the x-axis is described by the function x(t) = A t + B t2,

where t is in seconds, x is in meters, and the constants A and B are given below.

Randomized Variables
A = -4.1 m/s
B = 5.4 m/s2Part (a) Enter an expression, in terms of A, B, and t, for the velocity of the particle as a function of time. Part (b) At what time, in seconds, is the particle’s velocity zero?

Answer 1

Answer

given,

x(t) = A t + B t²

A = -4.1 m/s

B = 5.4 m/s²

a) velocity of the particle is equal to the differentiation of Position w.r.t. time

  $\dfrac{dx}{dt}=\dfrac{d}{dt}(-4.1 t + 5.4 t^2)$

  $v =-4.1 + 2\times 5.4 t$

  $v = -4.1 + 10.8 t$

the above equation gives the function of velocity.

b) time at which velocity of particle is zero

 v = -4.1 + 10.8 t

inserting v = 0 and calculating v

 0 = -4.1 + 10.8 t

 10.8 t = 4.1

   t = 0.38 s

time at which velocity is zero is equal to 0.38 s.