The acceleration of the particle at time t is:

The velocity of the particle at time t is given by the integral of the acceleration a(t):

and the position of the particle at time t is given by the integral of the velocity v(t):

Assuming the particle starts from position x(0)=0 at t=0, the distance the particle covers in the first t=2 seconds can be found by substituting t=2 s in the equation of x(t):
 
 
        
        
        
A box is sliding up an incline that makes an angle of 14.0° with respect to the horizontal. the coefficient of kinetic friction between the box and the surface of the incline is 0.180. the initial speed of the box at the bottom of the incline is 2.20 m/s. how far does the box travel along the incline before coming to rest?
        
             
        
        
        
Answer:
10 km/hr/s
Explanation:
The acceleration of an object is given by

where
v is the final velocity
u is the initial velocity
t is the time
For the car in this problem:
u = 0

t = 6 s
Substituting in the equation,

 
        
             
        
        
        
Answer: Velocity terminal = 0.093m/s
Explanation:
1. We start by evaluating the gap distance between the two cylinders as h = R(sleeve) - R(cylinder)
 = (0.0604/2 - 0.06/2)m
 = 2×10^-4
Surface are of the cylinder in the drop, which is required in order to evaluate the shearing stress can be expressed as A(cylinder) = π.d.L
= (π×0.06×0.4)m²
= 0.075m²
Since the force of the cylinder's weight is going to balance the shearing force on the walls, we can express the next equation and derive terminal velocity from it.
Shearing stress = u×V.terminal/h = 0.86×V/0.0002
= 4300Vterminal
Therefore, Fw = shearing stress × A
30N = 4300Vterminal × 0.075
V. terminal = 30/4300 m.s
V. terminal = 0.093m/s