Motorcycle Catches a Car (Acceleration)

In summary, the problem involves a motorcycle and a car traveling at constant speed on a straightaway. The motorcycle starts to accelerate at a certain time and eventually catches up with the car, traveling at twice the car's speed. The distance traveled by the motorcycle from the moment it starts to accelerate until it catches up with the car can be found by using the formulas for time and distance traveled. After solving for the variables, it is found that the distance traveled by the motorcycle is 54 meters. The conversation also includes the calculations and struggles of the person trying to solve the problem.
  • #1
Kalie
46
0
A motorcycle is 27 m behind a car that is traveling at constant speed on a straightaway. Initially, the car and the motorcycle are both traveling at the same speed, . At some time , the motorcycle starts to accelerate at a rate of . By the time the motorcycle catches up with the car, at time , it is traveling at twice the car's speed.

I solved all of the parts except for the last one

How far did the motorcycle travel from the moment when it starts to accelerate (at time ) until it catches up with the car (at time )?

The problem is I don't know how to start it

I found that Vcar= 18m/s and t2-tl=3s

and so Vmoto=36m/s

but i don't know what is wrong...

please help I have been working on this problem for about 4 hours...I think I'm going to burst:cry:
 
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  • #2
For the motorcycle we have from v = u + at that

[tex]t_c = \frac{v_o}{a}[/tex]

where tc is the time to close the gap and vo is the intial speed of the two. Then the distance the motorcycle traveled until it caught up with the car is given by

[tex]v_ot_c + 0.5a{t_c}^2 = 27 + v_ot_c[/tex]

the term on the right is the gap plus the extra distance the car traveled during the time tc. This gives

[tex]\frac{{v_o}^2}{a} = 54[/tex]

using the previous formula for tc. Now the distance the motorcycle traveled can be found from

[tex]v^2 = u^2 + 2as[/tex]
 
Last edited:
  • #3
Awesome thank you
 

1. What is meant by "Motorcycle Catches a Car (Acceleration)"?

"Motorcycle Catches a Car (Acceleration)" is a phrase used to describe an experiment or scenario in which a motorcycle and a car are involved in a race or pursuit, and the motorcycle is able to catch up to or overtake the car due to its faster acceleration.

2. How is acceleration measured in this scenario?

In this scenario, acceleration is measured in meters per second squared (m/s²). This is a unit of measurement for the rate at which an object's velocity changes over time.

3. What factors affect the acceleration of a motorcycle and a car?

The acceleration of a motorcycle and a car can be affected by several factors, including the engine power, weight of the vehicle, aerodynamics, and traction of the tires. In this scenario, the motorcycle's lighter weight and potentially more powerful engine may give it an advantage in terms of acceleration.

4. Can a motorcycle always catch a car in a race or pursuit?

No, it is not guaranteed that a motorcycle will always be able to catch a car in a race or pursuit. While a motorcycle may have a faster acceleration, a car may have a higher top speed or better handling, allowing it to maintain a distance or even overtake the motorcycle in certain situations.

5. How can the results of this scenario be applied in real life?

The results of this scenario can be applied in real life to understand the importance of acceleration in a race or pursuit. It also highlights the potential advantages and disadvantages of different vehicles in terms of acceleration, and how it can impact the outcome of a race or pursuit.

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