Step-by-step explanation:
First, let's calculate the work done by the force applied by Taylor.
Wt = Fd = (1.3 x 10⁴ N)(15 m) = 195000 J
Because the work is the force times the distance.
Now, to calculate the force of friction, we get:
Ff = (Fn)μ = mgμ
Ff = (1200kg)(9.8 m/s²)(0.67)
Ff = 7879.2 N
Where Fn is the normal force and it is equal to the weight of the car. m is the mass and g is the acceleration due to gravity.
Then, the work done by the friction is
Wf = Ff d = (7879.2 N)(15 m) = 118188 J
Therefore, the net work is equal to
Wnet = Wt - Wf
Wnet = 195000J - 118188 J
Wnet = 76812 J
To find the acceleration, we need to find the net Force
Fnet = F - Ff
Fnet = 13000N - 7879.2N
Fnet = 5120.8 N
So, by the second law of Newton, the acceleration is equal to
a = Fnet/m
a = 5120.8 N / 1200 kg
a = 4.27 m/s²
Finally, by the kinematics equations, we get:
d = vt + (1/2)at²
Since it starts from rest, we get:
d = (1/2)at²
Solving for t, we get:
2d = at²
2d/a = t²
t = √(2d/a)
So, replacing d