Answer:
The total distance traveled by the truck is 1797 m
Step-by-step explanation:
Hi there!
The equation of position and velocity of an object moving in a straight line with constant acceleration are the following:
x = x0 + v0 · t + 1/2 · a · t²
v = v0 + a · t
Where:
x = position of the truck at time t.
x0 = initial position.
v0 = initial velocity.
a = acceleration.
t = time
v = velocity at time t.
Let's calculate the position of the truck after the first 14.0 s:
x = x0 + v0 · t + 1/2 · a · t²
If we place the origin of the frame of reference at the first stop light, the initial position, x0, is zero. Since the truck starts from rest, v0 = 0. So, the equation of position will be:
x = 1/2 · a · t²
x = 1/2 · 1.60 m/s² · (14.0 s)²
x = 157 m
Then, the truck travels with constant speed (a = 0) for 70.0 s. The equation of position will be:
x = x0 + v · t
In this case, let's consider the initial position as the the position where the car is after 14.0 s (157 m from the stop light). The velocity is the velocity reached after the 14.0 s of acceleration. Let's calculate it with the equation of velocity:
v = v0 + a · t (v0 = 0)
v = 1.60 m/s² · 14.0 s
v = 22.4 m/s
So, the position will be:
x = 157 m + 22.4 m/s · 70.0 s
x = 1725 m
Now, the truck slows down with an acceleration of 3.50 m/s² until it stops (until its velocity is zero). Let's calculate the time at which the velocity of the truck is zero:
v = v0 + a · t
0 = 22.4 m/s - 3.50 m/s² · t
-22.4 m/s / -3.50 m/s² = t
t = 6.4 s
Now let's calculate the position of the truck after that time considering the initial position as the position at which the truck was after the 70.0 s traveling at constant speed (1725 m from the stop light):
x = x0 + v0 · t + 1/2 · a · t²
x = 1725 m + 22.4 m/s · 6.4 s + 1/2 · (-3.50 m/s²) · (6.4 s)²
x = 1797 m
The total distance traveled by the truck is 1797 m