Motion in one dimension problem

In summary: Using the information given, we can plug in the values and solve for the distance traveled by the police car after accelerating for 5.00 seconds:d = (85 m/s)*(5.00 s) + (1/2)*(3.00 m/s^2)*(5.00 s)^2= 425 m + 37.5 m= 462.5 mThis is the distance traveled by the police car before it overtakes the speeder. To find the speeder's speed,
  • #1
vv_ramirez259
3
0

Homework Statement



An unmarked police car traveling a constant 85 is passed by a speeder. Precisely 1.00 after the speeder passes, the police officer steps on the accelerator. If the police car accelerates uniformly at 3.00 and overtakes the speeder after accelerating for 5.00 , what was the speeder's speed?

Homework Equations



vf = vo + at
avg velocity = (vf + vo) /2
d = vo)t + (1/2) at2
vf2 = vo2 + 2ad

The Attempt at a Solution



I found that t=1s, a= 23.6 m/s2.. I am unsure what formula to use
 
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  • #2
vv_ramirez259 said:

Homework Statement



An unmarked police car traveling a constant 85 is passed by a speeder. Precisely 1.00 after the speeder passes, the police officer steps on the accelerator. If the police car accelerates uniformly at 3.00 and overtakes the speeder after accelerating for 5.00 , what was the speeder's speed?

Homework Equations



vf = vo + at
avg velocity = (vf + vo) /2
d = vo)t + (1/2) at2
vf2 = vo2 + 2ad

The Attempt at a Solution



I found that t=1s, a= 23.6 m/s2.. I am unsure what formula to use
Draw a distance time graph for the police car. Let the time the speeder passes the police car be the origin. At t=6, what is d?

Now you can draw the graph for the speeder. What two points do you have for the speeder's graph? What kind of graph is it? What physical quantity does the slope relate to?

BTW, what units of distance are you using? 85 m/sec is about 200 mph.

AM
 
  • #3
to solve for the speeder's initial velocity.

To solve for the speeder's initial velocity, we can use the equation vf = vo + at. In this case, the final velocity (vf) will be the police car's speed when it overtakes the speeder, which is 85 m/s. The acceleration (a) is given as 3.00 m/s2 and the time (t) is 5.00 seconds. Therefore, we can rearrange the equation to solve for the initial velocity (vo):

vo = vf - at
vo = 85 m/s - (3.00 m/s2)(5.00 s)
vo = 85 m/s - 15 m/s
vo = 70 m/s

Thus, the speeder's initial velocity was 70 m/s before the police car accelerated and caught up to them.
 

FAQ: Motion in one dimension problem

What is the definition of motion in one dimension?

Motion in one dimension refers to the movement of an object along a single straight line. This can be represented by a one-dimensional coordinate system, where the position of the object is described by a single value.

How is the position of an object in one dimension calculated?

The position of an object in one dimension is calculated by measuring the distance between the object and a chosen reference point. This distance is known as displacement and is usually represented by the symbol "x". The position of the object can change as it moves along the one-dimensional line, and this change is known as its displacement.

What is the difference between speed and velocity in one dimension?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. In one dimension, speed can be calculated by dividing the distance traveled by the time taken, while velocity can be calculated by dividing the displacement by the time taken.

How do you calculate acceleration in one dimension?

Acceleration is a measure of how quickly an object's velocity changes over time. In one dimension, acceleration can be calculated by dividing the change in velocity by the change in time. It is typically represented by the symbol "a". If an object is increasing its velocity, the acceleration is positive, while if it is decreasing its velocity, the acceleration is negative.

What is the difference between average and instantaneous velocity in one dimension?

Average velocity is the overall velocity of an object over a certain period of time, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity can be calculated by dividing the total displacement by the total time taken, while instantaneous velocity can be calculated by finding the slope of the object's position-time graph at a specific point.

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