Answer:
18 m/s
Explanation:
Force is given by mass × acceleration
F = ma
a = F/m
For the first 11.0 m, there is no friction. Hence, the constant force is applied fully on the crate. The acceleration is
a = 225/26.0 m/s²
By the equation of motion, v² = u² + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance travelled.
Using the values for the first part of the motion,
v² = 0² + 2 × 8.65 × 11.0
v = 13.8 m/s
This is the initial velocity for the second part of the motion. This part has friction of coefficient 0.20.
The frictional force = 0.20 × weight = 0.20 × 26.0 × 9.8 = 50.96 N
The effective force moving the crate in the second motion = 225 - 50.96 N = 174.04 N
This gives an acceleration of 174.04/26.0 = 6.69 m/s².
Using parameters for the equation of motion, v² = u² + 2as
v² = 13.8² + 2 × 6.69 × 10 = 324.24
v = 18 m/s
