Solve Acceleration Problem: Plot Distance vs Time

In summary, the maximum deceleration of a car on a dry road is 8.0 m/s^2. Two cars traveling at 55 mi/h will not collide if their drivers apply their brakes when they are 85m apart, as they will be 10 m apart when they stop. To plot the distance versus time for both cars, use the formula d = (1/2)at^2 and label the position versus time plot of the car with positive velocity as x_1(t). The solution for part b can be found by using the same formula to find the distance at a series of times and plotting them on a graph.
  • #1
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Homework Statement


The maximum deceleration of a car on a dry road is about 8.0 m/s^2.
a. If two cars are moving head-on toward each other at 55 mi/h, and their drivers apply their brakes when they are 85m apart, will they collide?
On the same graph, plot distance versus time for both cars.
Assume x = 0 is the midpoint between the cars and t = 0 when the brakes are applied. Label the position versus time plot of the car with the positive velocity as x_1(t).


Homework Equations





The Attempt at a Solution


a. no they will not collide, they will be 10 m apart when they stop.
b. i think...
(0,-42.5) and (3,-5) for x_1(t)
and (0,42.5) and (3,5) for x_2(t)
 
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  • #2
I get a little more than 10 - closer to 11 m apart.
 
  • #3
how would part b be solved?
 
  • #4
Use the same d = formula to find the distance at a series of times and plot them on a graph.
 

Related to Solve Acceleration Problem: Plot Distance vs Time

1. What is acceleration and how is it related to distance and time?

Acceleration is the rate of change of an object's velocity over time. It is related to distance and time through the formula a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

2. How do you solve an acceleration problem?

To solve an acceleration problem, you first need to identify the given values, such as initial and final velocities and time. Then, use the formula a = (vf - vi)/t to calculate the acceleration. Finally, plot the distance vs time graph to visualize the relationship between the two variables.

3. What is the purpose of plotting distance vs time in an acceleration problem?

The purpose of plotting distance vs time is to show the relationship between the two variables and to help visualize the acceleration of an object. The slope of the line on the graph represents the acceleration, and the y-intercept represents the initial velocity.

4. How can I determine the acceleration of an object from a distance vs time graph?

The acceleration of an object can be determined by finding the slope of the line on the distance vs time graph. The steeper the slope, the greater the acceleration. You can also use the formula a = (vf - vi)/t, where vf is the final velocity and vi is the initial velocity.

5. How does acceleration affect an object's motion?

Acceleration affects an object's motion by changing its velocity over time. If an object has a positive acceleration, it will speed up, and if it has a negative acceleration, it will slow down. The magnitude of the acceleration also determines how quickly the object's velocity changes.

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