Answer
given,
v = (6 t - 3 t²) m/s
we know,


position of the particle

integrating both side

x = 3 t² - t³
Position of the particle at t= 3 s
x = 3 x 3² - 3³
x = 0 m
now, particle’s deceleration


a = 6 - 6 t
at t= 3 s
a = 6 - 6 x 3
a = -12 m/s²
distance traveled by the particle
x = 3 t² - t³
at t = 0 x = 0
t = 1 s , x = 3 (1)² - 1³ = 2 m
t = 2 s , x = 3(2)² - 2³ = 4 m
t = 3 s , x = 0 m
total distance traveled by the particle
D = distance in 0-1 s + distance in 1 -2 s + distance in 2 -3 s
D = 2 + 4 + 2 = 8 m
average speed of the particle



Because when a candle burns the wax is burning off so as its heated more and more wax is lost and if more wax is lost... Obviously it means that the candles mass will be lower :)
Answer:
Part a)

Part b)

Explanation:
Force applied by the student on the box is 80 N at an angle of 25 degree
so here two components of the force on the box is given as




now in vertical direction we can use force balance for the box to find the normal force on it



now kinetic friction on the box opposite to applied force due to rough floor is given as


now the net force on the box in forward direction is given as


now the acceleration of the box is given as


Part b)
when box is pulled up along the inclined surface of angle 10 degree
now the two components of the force will be same along the inclined and perpendicular to inclined plane


now force balance perpendicular to inclined plane is given as


now the friction force opposite to the motion on the box is given as


now the net pulling force along the inclined plane is given as



now the box will decelerate and it is given as

