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Answer :
Final answer:
It will take the car approximately 11.17 seconds to catch up with the truck that passes it traveling at a constant speed when the car starts from rest and accelerates at 2.9 m/s².
Explanation:
The question asks how long it takes for a car that starts from rest with a constant acceleration to catch up with a truck traveling at a constant speed. The car accelerates from rest at 2.9 m/s², while the truck travels at a constant speed of 36.3 mph, which is approximately 16.2 m/s (1 mph equals approximately 0.44704 m/s).
To solve this problem, we need to consider that the car and truck will have traveled the same distance when the car catches up to the truck. The equations for distance for the car (with acceleration) and the truck (traveling at constant speed) are:
- Distancecar = ½ * acceleration * time²
- Distancetruck = speed * time
We set the distances equal to each other:
½ * 2.9 m/s² * time² = 16.2 m/s * time
This gives us a quadratic equation:
½ * 2.9 * time² - 16.2 * time = 0
Factoring out the common term 'time', we get:
time(½ * 2.9 * time - 16.2) = 0
Ignoring the solution where time equals zero (since we want to know how long it takes after they have started moving), we get:
½ * 2.9 * time = 16.2
time = (16.2 / (0.5 * 2.9)) seconds
Solving this, time ≈ 11.17 seconds
Therefore, it will take the car approximately 11.17 seconds to catch up with the truck.
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Answer:
It take the car to catch up with the truck 111.91 s.
Explanation:
To solve this problem we have to use the formula for uniformly accelerated motion (for the car) and the formula for uniform rectilinear movement (for the truck).
We apply the corresponding formula for each vehicle, so we will have two equations. As the question is how much time, time is the unknown variable that we will call t from now on.
Equation for the car is:
[tex]x_{c}=\frac{1}{2}*a*t^{2}[/tex]
Equation for the truck is
[tex]x_{t} =v*t[/tex]
We know that t will be the same for the two vehicle on the instant the car catch up the truck.
On the time t the distance x traveled for both cars are the same, so we can equate the two formulas ans isolate t.
[tex]v*t=\frac{1}{2} *a*t^{2} \\t=(2*v)/a\\t=111,91s[/tex]
Note: all unit of measurement must be the same, for speed, we need to convert 36,3mph to m/s.
36,3mph=162.27m/s we use 162.27m/s in the formulas.
