Bike and Car both accelerate from rest ( intermediate problem)

In summary, the problem involves a bike and a car starting from rest and accelerating with different constant rates. The bike has a higher acceleration and reaches a final velocity of 20 mi/hr while the car has a lower acceleration and reaches a final velocity of 50 mi/hr. The problem asks for the time it takes for the car to catch up to the bike and the maximum distance the bike can be ahead of the car before the car catches up. The solution involves calculating the times and distances at specific events where both the bike and car switch from accelerated motion to constant velocity motion.
  • #1
Color_of_Cyan
386
0
Bike and Car both accelerate from rest ("intermediate" problem)

Homework Statement


Basically, both a bike and car start from rest. The bike will not go any faster than (final velocity) 20 mi / hr. The car will not go faster than (final velocity) 50 mi / hr. However, at first, the bike is ahead of the car because it has a constant acceleration of 13 mi / (hr s), which is higher than that of the car's constant acceleration of 9 mi / (hr s).


Part a: What is the time it takes for the car to catch up to (and have the same position of) the bicycle.

Part b: What is the MAXIMUM DISTANCE of the bike being ahead of the car before the car has the same velocity of the bike and starts to catch up?

Homework Equations


Vf = Vi + at

Vf2 = Vi2 + 2a(Xf - Xi)

Xf = Xi + Vi t + 1/2 at2

etc



The Attempt at a Solution


initial velocity of car and bike = 0

acceleration of bike = 13 mi / hr s

FINAL velocity of bike = 20 mi / hr s

FINAL velocity of car = 50 mi / hr s

Is it possible to solve this problem without the use of calculus? If I do, how would I apply it to here. Anyways, for part a if I substitute Xf = Xi + Vi t + 1/2 at2 (plugging whatever is the acceleration of the bike) equal to xf = (whatever is the acceleration of the car), then I would just end up with t as a variable and then t would just cancel out, which I do not want.

However for the car, using vf = vi + at, and then 20 mi / hr = 0 + [(20 mi / (hr s) ]t it will take the CAR 2.23 seconds to reach the SAME VELOCITY as the BIKE, but this is not what I want to solve for. I know I would probably have to improvise somewhere, but where?
 
Last edited:
Physics news on Phys.org
  • #2


I suggest that you first calculate the times and distances for certain "events" that take place, namely the times and distances from the start when the bike and car switch over from accelerated motion to constant velocity motion. What are the positions of car and bike at each of these events?
 

1. How does the acceleration of a bike compare to that of a car?

The acceleration of a bike is typically slower than that of a car. This is due to the fact that bikes have smaller engines and less weight, resulting in less force to propel them forward.

2. Do both a bike and car accelerate at the same rate?

No, bikes and cars have different acceleration rates. Cars usually have more powerful engines and greater mass, allowing them to accelerate faster than bikes.

3. Can a bike accelerate faster than a car?

In general, cars have a higher maximum acceleration than bikes. However, some high-performance bikes may be able to accelerate faster than certain cars.

4. How does the acceleration of a bike and car affect their fuel efficiency?

The acceleration of a vehicle can greatly impact its fuel efficiency. Bikes are generally more fuel-efficient than cars due to their smaller engines and lighter weight, which requires less energy to accelerate.

5. What factors can affect the acceleration of a bike and car?

The acceleration of a bike and car can be influenced by various factors such as engine power, weight, aerodynamics, road conditions, and tire grip. These factors can affect the amount of force and traction needed for acceleration.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
698
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
2
Replies
45
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
622
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
8K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
1K
Replies
7
Views
2K
Back
Top