A motorcycle catches a car after accelerating

In summary, the motorcycle and car initially travel at the same speed of 22.0 m/s and are 60.0 m apart. After 5.00 seconds, the motorcycle starts accelerating at a rate of 5.00 m/s^2 and catches up with the car at 4.90 seconds. The motorcycle travels a distance of 168 meters during this time. The 5 second wait period does not affect the overall time it takes for the motorcycle to catch up with the car. The equation d=Xo+VoT+1/2aT^2 can be used to solve for time, velocity, acceleration, and distance in this problem.
  • #1
Pioneer98
19
0
A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 22.0 m/s , and the distance between them is 60.0 m . After t1= 5.00 s , the motorcycle starts to accelerate at a rate of 5.00 m/s^2 . The motorcycle catches up with the car at some time .

How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2-t1.

How far does the motorcycle travel from the moment it starts to accelerate (at time t1) until it catches up with the car (at time t2)? Should you need to use an answer from a previous part, make sure you use the unrounded value.


d=Xo+VoT+1/2aT^2

I plugged distance initial velocity acceleration and time. When I got the distance I divide it by the speed it was traveling and got the time to be 5.57 seconds.
 
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  • #2
What part does the 5 second 'wait' period play in the problem?
 
  • #3
You want the overall time subtracted from the first time so you can get the time it accelerated to the car.
 
  • #4
You're interested in the time takes to catch up to the car, right?
So that first 5 seconds can be discarded, because in those 5 seconds no other conditions are changing.
 
  • #5
Oh ok gotcha now. I got 4.90 seconds for the time it takes the motorcycle to catch the car.
 
  • #6
That's right! :smile:
 
  • #7
Finally :) so for the other part of the problem I want to get the speed and use the time from the previous answer to figure out the distance traveled? I get speed/velocity by using V=Vo+aT
 
  • #8
You can do that, but I find that to be a useless calculation.

What equation relates time, vo, acceleration, and distance?
 
  • #9
d=Xo+VoT+1/2aT^2 ?
 
  • #10
Yessir. Using that should give you the right answer.
 
  • #11
Alright thanks for the help!
 
  • #12
Just curious, what'd you get?
 
  • #13
168 meters
 

1. How is it possible for a motorcycle to catch a car after accelerating?

It is possible for a motorcycle to catch a car after accelerating because motorcycles have a higher power-to-weight ratio and are more aerodynamically efficient than cars. This means they can accelerate faster and reach higher speeds in a shorter amount of time.

2. What factors contribute to a motorcycle being able to catch a car after accelerating?

The factors that contribute to a motorcycle being able to catch a car after accelerating include the motorcycle's weight, engine power, aerodynamic design, and the skill of the rider in controlling the bike.

3. Can any type of motorcycle catch a car after accelerating?

Not all motorcycles are capable of catching a car after accelerating. It depends on the specific make and model of the motorcycle and its performance capabilities.

4. How does the acceleration of a motorcycle compare to that of a car?

The acceleration of a motorcycle is usually faster than that of a car due to its lighter weight and more powerful engine. However, this can vary depending on the specific vehicles being compared.

5. Is it safe for a motorcycle to catch a car after accelerating?

In general, it is not safe for a motorcycle to catch a car after accelerating. Motorcycles are smaller and less visible on the road, making them more vulnerable to accidents. It is important for both motorcycle riders and car drivers to follow traffic laws and maintain a safe distance from each other on the road.

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