A particle P moves in a straight line starting from a point O and comes to rest 35 s later. At time t s after leaving O, the velocity v m s⁻¹ of P is given by v = (4/5)t² 0 ≤ t ≤ 5, v = 2t + 10 5 ≤ t ≤ 15, v = a + bt² 15 ≤ t ≤ 35, where a and b are constants such that a 0 and b

Question

A particle P moves in a straight line starting from a point O and comes to rest 35 s later. At time t s after leaving O, the velocity v m s⁻¹ of P is given by
v = (4/5)t²                      0 ≤ t ≤ 5,
v = 2t + 10                     5 ≤ t ≤ 15,
v = a + bt²                      15 ≤ t ≤ 35,
where a and b are constants such that a > 0 and b < 0.

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