Motion problem for constant acceleration of truck

In summary, a truck traveling at 28.0 m/s approaches a stationary car that pulls out into the slow lane with an acceleration of 2.6 m/s2. To determine how long it will take the truck to reach the car, the equation 1.3t2 - 28.0t + 125 = 0 is used, resulting in two possible solutions: t = 15.2 s or t = 6.32 s. To determine which value is correct, one must consider the velocities of each vehicle and the distances covered in the given time intervals.
  • #1
chroncile
35
0

Homework Statement


A truck travels at a constant speed of 28.0 m/s in the fast lane of a two-lane highway. It approaches a stationary car stopped a the side of the road. When the truck is still 125 m behind the car, the car pulls out into the slow lane with an acceleration of 2.6 m/s2. How long will it take the truck to reach the car? (Answer is 6.32 s)


Homework Equations


dt = dc + 125
dc = 1.3t2


The Attempt at a Solution


Okay I got the answer, but it's in quadratic form so:

1.3t2 - 28.0t + 125 =

t = 15.2 s or t = 6.32 s

How do you know which answer is the correct one?
 
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  • #2
Hello? Please, I need help :frown:
 
  • #3
How did you come up with your equation? You must have started from the basic kinematic equations, right?

Go back to those and try both values of t to see which one works/makes more sense.
 
  • #4
Think about what this means...

At the end of t=6.32s, how fast is each vehicle moving (what are their velocities)?
What is the distance covered by each in this time interval?

What about at t=15.2s?
 

FAQ: Motion problem for constant acceleration of truck

1. How do you calculate the distance traveled by a truck with constant acceleration?

To calculate the distance traveled by a truck with constant acceleration, you can use the formula: d = v0t + ½at2 where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration.

2. What is the equation for finding the final velocity of a truck with constant acceleration?

The equation for finding the final velocity of a truck with constant acceleration is: v = v0 + at where v is the final velocity, v0 is the initial velocity, t is the time, and a is the acceleration.

3. Can the acceleration of a truck change during motion?

Yes, the acceleration of a truck can change during motion. This is known as variable acceleration, where the rate of change of velocity is not constant. In this case, the equations for constant acceleration cannot be used and more complex equations are needed to calculate the truck's motion.

4. How does the mass of the truck affect its acceleration?

The mass of the truck does not directly affect its acceleration. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the applied force and inversely proportional to its mass. Therefore, a heavier truck will require more force to accelerate at the same rate as a lighter truck.

5. What is the difference between average acceleration and instantaneous acceleration?

The average acceleration of a truck is the change in velocity over a given time period, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration can be calculated by dividing the change in velocity by the change in time, while instantaneous acceleration can be calculated by taking the derivative of the velocity function with respect to time.

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