Question

3. A particle is projected to the right from the position S = 0, when an initial velocity of 8 m/s. If the acceleration of the particle is defined by the relation a = -0.5 v3/2, where a in m/s2 and v in m/s. Determine a) the distance the particle will have traveled when its velocity is 5 m/s b) the time when v = 1m/s c) the time require for the particle to travel 8m

Answer 1

a) 3.5 m

b) 14 secs

c) 1.4 secs

Step-by-step explanation:

a) Determine the distance the particle will travel

given velocity ( final velocity ) = 5 m/s

v^2 = u^2 + 2as

s = ( v^2 - u^2 ) / 2a

= ( 5^2 - 8^2 ) / 2 ( -0.5 * 5^3/2 )

= 3.5 m

b) Determine the time when v = 1m/s

V = u + at

1 = 8 + ( -0.5 * 1^3/2 ) * t

∴ t = 14 secs

c) Determine the time required for particle to travel 8 m

we will employ both equations above

V^2 = u^2 + 2as

s = 8 m , V = unknown , u = 8 m/s back to equation

V^2 = 8^2 + 2 ( - 1/2 * V^3/2 ) * 8

∴ V^2 + 8V^3/2 - 64 = 0

resolving the above equation

V = 3.478 m/s

now using the second equation

V = u + at

3.478 = 8 + ( - 1/2 * 3.478^3/2 ) * t

hence : t = 1.4 secs