A particle travels so that its distance D (in metres) from its origin O is modelled by the equation D = 24 + 15t - [tex]\frac{t^{2} }{2}[/tex], where t is the time in minutes after the particle has started to move.

a. calculate the particle's distance from O when it first started to move.

b. determine the time when the particle first reaches O. Give your answer to 2 decimal places.

c. determine the particle's speed when it has been moving for 3 minutes. Give your answer in m [tex]S^{-1}[/tex]

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onyebuchinnaji onyebuchinnaji · Answer 1 · 2022-07-26T20:33:18+02:00

(a) The particle's distance from O when it first started to move is 24 m.

(b) The time when the particle first reaches O is 15 mins.

(c) The particle's speed when it has been moving for 3 minutes is 0.2 m/s.

D = 24 + 15 - t²/2

when the time, t = 0

D = 24 m

When the object reaches O, its final velocity, v = 0

v = dD/dt

v = 15 - t

0 = 15 - t

t = 15 mins

v = 15 - t

v = 15 - 3

v = 12 m/min

v = 12 m/min x 1min/60s = 0.2 m/s

Thus, the particle's distance from O when it first started to move is 24 m.

The time when the particle first reaches O is 15 mins.

The particle's speed when it has been moving for 3 minutes is 0.2 m/s.

Learn more about speed here: https://brainly.com/question/6504879

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