An automobile and a truck start from rest?

a)
Consider the truck :
Displacement, s = 46.0 m
Acceleration, a = 2.20 m/s²
Initial velocity, u = 0 m/s

s = ut + (1/2)at²
46.0 = 0 + (1/2) × 2.20 × t²
t = √(2 × 46.0 / 2.20) s
t = 6.47 s

As the truck and the automobile start at the same time,
time taken for the automobile to overtake the truck = 6.47 s


====
b)
Consider the automobile :
Acceleration, a = 3.50 m/s²
Initial velocity, u = 0 m/s
Time taken, t = 6.47 s

s = ut + (1/2)at²
s = 0 + (1/2) × 3.5 × 6.47² m
s = 73.3 m

Distance that the automobile behind the truck initially
= (73.3 - 46.0) m
= 27.3 m


====
c)
Consider the truck :
Displacement, s = 46.0 m
Acceleration, a = 2.20 m/s²
Initial velocity, u = 0 m/s

v² = u² + 2as
v² = 0 + 2 × 2.2 × 46.0
v = √(2 × 2.2 × 46.0) m/s
Speed of the truck when they are abreast, v = 14.2 m/s


====
d)
Consider the automobile :
Acceleration, a = 3.50 m/s²
Initial velocity, u = 0 m/s
Time taken, t = 6.47 s

v = u + at
v = 0 + 3.5 × 6.47 m/s
Speed of the automobile when they are abreast = 22.6 m/s

Let’s use the following equation to determine the time for the truck to move 46 meters.


d = vi * t + ½ * a * t^2, vi = 0
46 = ½ * 2.2 * t^2
t = √(46 ÷ 1.1)

This is approximately 6.47 seconds. This is the time when the automobile and truck are at the same position. Let’s use the same equation to determine the distance the automobile moves during this time.

d = ½ * 3.50 * 46 ÷ 1.1 = 80.5 ÷ 1.1

This is approximately 73.18 meters. b)How far was the automobile behind the truck initially?

To determine the initial distance between the automobile and the truck, subtract 46 meters from this distance.


d = 80.5 ÷ 1.1 – 46

This is approximately 27.18 meters. To be at the same position, the automobile must move approximately 27.18 meters more than the truck moves. To determine the speed at time they are abreast, use the following equation.


vf = vi + a * t, vi = 0

For the truck, vf = 2.20 * √(46 ÷ 1.1)
This is approximately 14.2 m/s

For the automobile, vf = 3.50 * √(46 ÷ 1.1)
This is approximately 22.6 m/s. I hope this is helpful for you.

Assuming both vehicles maintain their constant acceleration until they are abreast of each other:
The time interval measured from the start = t
For truck, the distance from start to when vehicles are abreast of each other is: Dt = 1/2(2.20)t²
For auto, the distance from start to when vehicles are abreast of each other is: Da = 1/2(3.50)t²
46 = 1/2(2.20)t²
t² = 46.0/1.10 = 41.818...
t ≈ = 6.47 s ANS a)
Da = 1/2(3.50)(6.466697907)² ≈ 73.2 m ANS b)
speed of truck when abreast = Vt = at = (2.20)(6.4667) ≈ 14.2 m/s ANS c)
speed of the auto when abreast = Va = at (3.50)(6.4667) ≈ 22.6 m/s ANS d)