Aspeedboat starts from rest and accelerates at - 2.01 m/s2 for 7.00 s. at the end of this time, the boat continues for an additional 6.00 s with an acceleration of +0.518 following this, the boat accelerates at 1.49 m/s2 for 8.00 s (a) what is the velocity of the boat at t = 21.0 s? (b) find the total displacement of the boat

velocity after 21 sec =  0.96 m/s

total displacement =  164.341 m

Explanation:

given data

accelerates = - 2.01 m/s²

time = 7 s

additional time = 6 s

acceleration = +0.518 m/s²

following boat accelerates = 1.49 m/s²

time = 8 s

to find out

velocity of the boat at time 21 s and the total displacement of the boat

solution

we find velocity after 7 second

velocity = accelerate × time

velocity after 7 sec = - 2.01 × 7 = -14.07 m/s

displacement = ut + 0.5 × at²

here u is initial speed = 0 and a is acceleration and t is time

displacement =   0.5 × (-2.01) (7)² = - 49.245 m

and

velocity after (7 + 6) = 13 second is

velocity after 13 sec = -14.07 +  ( 6 × 0.518)  = -10.96 m/s

displacement = ut + 0.5 × at²

here u is initial speed = -14.07  and a is acceleration and t is time

displacement =  -14.07 (6) +  0.5 × (0.518) (6)² = - 75.096 m

and

velocity after (7 + 6 + 8) = 21 second is

velocity after 21 sec = -10.96 + 1.49 × 8 = 0.96 m/s

displacement =  -10.96 (8) +  0.5 × (1.49) (8)² = - 40 m

so

total displacement = sum of all displacement

total displacement = (- 49.245) + (- 75.096) +  (- 40) = -164.341

total displacement =  164.341 m

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2