Answer:
The total distance is 130.2 [m]
Explanation:
In order to solve this problem we must use the expressions of kinematics. The clue to solve this problem is that the cart starts from rest, i.e. its initial speed is zero.
[tex]v_{f} =v_{o} +(a*t)[/tex]
where:
Vf = final velocity [m/s]
Vo = initial velocity = 0
a = acceleration = 3 [m/s²]
t = time = 8[s]
Vf = 0 + (3*8)
Vf = 24 [m/s]
With this velocity we can calculate the displacement using the following expression.
[tex]v_{f} ^{2} =v_{o} ^{2} +2*a*x[/tex]
where
x = distance traveled [m]
24² = 0 + (2*3*x)
x = 576/(6)
x = 96 [m]
Note: The positive sign in the equations is because the car is accelerating, it means its velocity is increasing.
The other important clue to solve this problem in the second part is that the final velocity is now the initial velocity.
We must calculate the final velocity.
[tex]v_{f}= v_{i} -(a*t)[/tex]
Vf = final velocity [m/s]
Vi = initial velocity = 24 [m/s]
a = desacceleration = 1.6 [m/s²]
t = time = 15 [s]
Vf = 24 - (1.6*15)
Vf = 21.6 [m/s]
With this velocity, we can calculate the displacement using the following expression.
[tex]v_{f} ^{2} =v_{o} ^{2} -2*a*x[/tex]
where
x = distance traveled [m]
21.6² = 24² - (2*1.6*x)
x = 109.44/(3.2)
x = 34.2 [m]
Note: The negative sign in the equations is because the car is desaccelerating, it means its velocity is decreasing.
Therefore the total distance is Xt = 34.2 + 96 = 130.2 [m].
