Part 1 At any time t seconds, the distance x metres of a particle moving in a straight line from a fixed point is given by x = 4 t 2 - 3 t + ln(1+3 t ) Determine expressions for the initial velocity...

Part 1

• At any time
  t
  seconds, the distance
  x
  metres of a particle moving in a straight line from a fixed point is given by

x
= 4t
²
-3t
+ ln(1+3t)

          Determine expressions for the initial velocity and acceleration of the particle

          and their values after 3 seconds.

• The displacement
  y
  centimetres of the side value of an engine is given by

y
= 3.2cos4pt
+ 4.5sin4pt

             Determine the precise velocity in metres per second when
t
=10 ms.