I have the answers. I need help with understanding the steps to get to the solution. Thank you.
1. a ) 0.0900 s^-2 . ( b ) +/- 16.97 mm/s.
2. -66.0 m, 149.0 m/s, 228 m/s^ 2 .
3. ( a ) 3.00 ft/s^ 4 . b ) v = ( t^2- 32) ft/s, x = ( t^4 /4- 32t + 64) ft
4. ( a ) 25.0 m/s. (b ) 19.00 m/s. (c) 36.8 m.
A particle oscillates between the points x = 40 mm and x = 160 mm with an acceleration a = k( 100 - x), where a and x are expressed in mm/ s^2 and mm, respectively, and k is a constant. The velocity of the particle is 18 mm/ s when x = 100 mm and is zero at both x = 40 mm and x = 160 mm. Determine (a) the value of k,( b) the velocity when x = 120 mm.
2. The motion of a particle is defined by the relation x = 1.5t^4 - 30t2 + 5t + 10, where x and t are expressed in meters and seconds, respectively. Determine the position, the velocity, and the acceleration of the particle when t = 4 s.
3. The acceleration of a particle is defined by the relation a = kt^2. (a) Knowing that v =-32 ft/ s when t = 0 and that v =-32 ft/ s when t = 4 s, determine the constant k. ( b) Write the equations of motion, knowing also that x = 0 when t = 4 s.
4. A truck travels 220 m in 10 s while being decelerated at a constant rate of 0.6 m/ s^2. Determine (a) its initial velocity, ( b) its final velocity, ( c) the distance traveled during the first 1.5 s.
This posting contains solution to the given problems.