3.111: Velocity from displacement with $\sqrt{2t + 1}$

0606/12/O/N/22 — Question 11 · 6 marks

A particle

P

moves in a straight line such that,

t

seconds after passing through a fixed point

O

, its displacement,

s

metres, is given by

s = \dfrac{(2t + 1)^{\frac{3}{2}}}{t + 1} - 1

(a)

Show that the velocity of

P

at time

t

can be written in the form

\dfrac{(2t + 1)^{\frac{1}{2}}}{(t + 1)^{2}}(a + bt)

, where

a

and

b

are integers to be found.

[5]

(b)

Show that

P

is never at instantaneous rest after passing through

O

[1]

3.111: Velocity from displacement with 2t+1\sqrt{2t + 1}2t+1​