Please explain both for first rating! ---1.) A particle moves along a straight l
ID: 3347379 • Letter: P
Question
Please explain both for first rating!
---1.) A particle moves along a straight line so that its acceleration at any given time t is a(t) = 2t-10 (in units of feet and seconds). If the initial velocity of the particle is 16 feet/sec, at what time t during the interval [0 ? t ? 7] does the particle change direction?
---2.) A stone is dropped o? a cli? and falls under gravity with a constant acceleration of ?32 ft/sec2. If it hits the ground with a speed of 160 ft/sec, determine the height of the cli?.
Explanation / Answer
a)
a(t) = 2t-10
v(t) = t^2 - 10t + c
v(0) = 16 => c = 16
particle change direction, v(0) = 0 => t^2 - 10t + 16 = 0 => (t-2)(t+8) = 0 => t = 2 (or) 8
but given 0< = t <= 7 => t = 2 sec
b)
v(0) = 0
v(t) = g*t
=> 160 = 32*t => t = 5 s
=> height of cliff = (1/2)*g*t^2 = 16*25 = 400 ft