1. An experiment done on the Moon shows the position of a particle moving along

Question

1. An experiment done on the Moon shows the position of a particle moving along they-axis vanes in time according to the expression Y(t)= 60+ t - 5t^2, where Y is in m and t is in seconds. (a) Determine the initial velocity, initial position and acceleration of the particle? (b) Write an expression and draw graphs of the position and velocity as a function of time? (c) Determine the acceleration, velocity and position of the particle at t = 10 S. d) What is the maximum height the object reaches and at what time does it reach this height?

Explanation / Answer

given position Y = 60 + t -5 t2

a) velocity v is

v= dy/dt

v = d(60 + t -5 t2 )/dt

v= (1-10t)m/s

accelaration is a

a = d2 y/ dt2

a = d(1-10t)/dt

a = -10 m/sec2

b)

c) t = 10 sec

then from the above velocity v = 1-10t

v = 1-10 X 10

v = 1-100

v = -99 m/s

and accelaration a = -10 m/s2

d)

h = 60+t-5t2

h = 60+10-5X102

h = 70-5X100

h= 70-500

h = 430m

t = -b/2a

y = 60+t-5t2

from the above equation a = -5 and b = 1

t = -1 / 2(-5)

t = 1 / 10

t = 0.1 sec

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