A speedboat 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