1.A bus travels 400 m between two stops. It starts from rest and accelerates at 1.50 m/s^2 until it reaches a velocity of 9.00 m/s. The bus continues at this velocity and then decelerates at 2 m/s^2 until it comes to a halt. Find the total time required for the journey.

Question

2.A 28-kg block is connected to an empty 1kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.45 and the coefficient of kinetic friction between the table and block is 0.32. Sand is gradually added to the bucket until the system just begins to move.
a)Calculate the amount of sand added to the bucket.
b)calculate the acceleration of the system.

Answer 1

1. find time toaccelerate
vf=a t
t= 9/1.5=6 seconds
then find time to deaccelerate
vf=vi+at
0=-vi/a +t t= 9/ 2= 4.5 seconds
now the distance it went at constant velocity
400=1/2 (1.5)*6^2 + 9 tc +9/2 * 4.5
400=27+9tc+10.1
tc=(400-27-10.1)/9=40.3 second
total time: 40.3+4.5+6 seconds.

check all that.

Answer 2

How did the 10.1 come about after the solving of 9/2*4.5?