Question

please see the attachment ​

Answer 1

Answer:

• Velocity at 4sec = 14m/s and velocity at 6sec = 20m/s.
• Average velocity between 4sec to 6sec = 32m/s.

Explanation:

• Velocity = dx/dt (differentiation of displacement gives us velocity)

                      = d(2+2t+3t²)/dt

                      = 0 + 2 +3t

                      = 2 + 3t.

Velocity at 4sec : t =4

 = 2 + 3 (4) (substitute 4 in place of 't' in the formula, 2+3t)

= 2 + 12

= 14m/s.

Velocity at 6sec : t = 6

= 2 + 3 (6)

= 2 + 18

= 20 m/s.

• Average velocity = total displacement/total time.

Displacement at 4sec = 2 + 2t + 3t²

                                    = 2 + 2(4) + 3(16)

                                     = 2+8+48

                                     = 58.

Displacement at 6sec = 2 + 2(6) + 3(36)

                                     = 2 + 12+ 108

                                     = 122.

Displacement between 4sec to 6sec = 122 - 58 =  64.

Total time between 4sec to 6sec  = 2sec.

Average velocity between 4sec to 6sec= 64/2 = 32m/s.