A particle travelling in a straight line passes a fixed point O with a velocity of 16 m/s. Its
acceleration, a m/s^2, is given by a = 12- 6t, where t is the time in seconds after passing O. Calculate
a) the greatest speed attained by the particle in the original direction of the motion.
b) The distance from O when t = 2
When t=0, the particle is at O, with velocity 16. So we substitute
t=0 and v=16
So the constant is 16, and
Use the vertex formula or differentiating and setting the derivative = 0
to find that the maximum velocity is
v=28 m/s when t=2 seconds. <--answer to (a)
To find the distance when t=2,
When t=0, the particle is at O, so at that instant the distance s=0, So
we substitute t=0 and s=0
So the constant is 0
We substitute t=2
s = 48 meters. <--answer to (b)
Edwin