Question

The displacement, s metres, of a moving particle after t seconds is given by
 
Determine the:  

1. velocity of the particle when t = 5:  
2. time, t seconds, when the particle is momentarily at rest; 
3. displacement, s metres, when the particle is momentarily at rest;
4. acceleration of the particle when t = 4 seconds. 

Answer 1

1. V=2t² − 7t − 6 iƒ t = 5
   =2t²−7t−6
   =9 m/s
2. V=2t²−7t−6 =0
   
   =4.212 s or -0.7122 s
   ∴ t = 4.212s
3. S= ²/₃t³ − ⁷/₂t² − 6t + 8 iƒ t = 4.212
   S= ²/₃t³ − ⁷/₂t² − 6t + 8
    =−37.5487m
4. a = ^dv/_dt = 4t − 7 iƒ t = 4
                =4 x 4 − 7
                 =9m/s²