The free body diagram representing this scenario is shown below
From the information given.
mass of car = 1200kg
Recall,
weight = mg
where
m = mass
g = acceleration due to gravity = 9.8 m/s^2
Thus,
weight of car = 1200 x 9.8 = 11760 N
Normal reaction, N has same magnitude with the weight but the direction is opposite. thus,
N = 11760 N
Frictional force = N x coefficient of friction
From the information given,
coefficient of friction = 0.67
Thus,
Frictional force = 11760 x 0.67 = 7879.2 N
Net force of the car = applied force - frictional force
applied force = 1.3 x 10^4 N = 13000 N
Thus,
Net force = 13000 - 7879.2 = 5120.8N
Recall,
net force = mass x acceleration
acceleration = net force/mass = 5120.8/1200 = 4.27 m/s^2
We want to calculate the time it will take Tyler to get to the gas station. We would apply one of Newton's equation of motion which is expressed as
s = ut + 1/2at^2
where
s = distance covered
t = time
a = acceleration
u = initial velocity
From the information given,
s = 15
a = 4.27
u = 0 because the car was at rest(Since it was broken down)
By substituting these values into the equation, we have
15 = 0 x t + 1/2 x 4.27 x t^2
15 = 0 + 2.135t^2
15 = 2.135t^2
Dividing both sides of the equation by 2.135, we have
15/2.135 = 2.135t^2
t^2 = 7.026
t = square root of 7.026
t = 2.65
The time required is 2.65 s
