(Acceleration) Car and Truck Problem

In summary, an automobile and a truck with initial positions and different accelerations are given. The truck has a constant acceleration of 2.10 m/s2 and the automobile has an acceleration of 3.4 m/s2. The automobile overtakes the truck after the truck has moved 50.0 m. The time it takes for the automobile to overtake the truck is 6.9 seconds. Initially, the automobile was 30.94 m behind the truck. Equations and data are also provided for solving the problem.
  • #1
XwyhyX
15
0
Here's the problem:

1. An automobile and a truck start from rest and at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s2, and the automobile an acceleration of 3.4 m/s2. The automobile overtakes the truck after the truck has moved 50.0 m. (a) How much time does it take the automobile to overtake the truck? (b) How far was the automobile behind the truck initially? (c) Draw the figure of the problem
2. Equations and Data : a=[itex]\frac{dV}{dt}[/itex] ; V = [itex]\frac{dx}{dt}[/itex]

CAR:
Acceleration = 3.4m/s2

TRUCK:
Acceleration = 2.10m/s2
Distance Traveled at time of overtaking = 50m
3. The Attempt at a Solution :
For a.)

Reading the problem, The time that the car overtook the truck should be the same as the overall time of the truck to cover 50m. So finding for t of the truck, I would have

[itex]\int[/itex]2.10dt = [itex]\int[/itex]dV

--Integrating this i would get

2.10t = V

I can solve for time using the equation for Velocity and 50 m as the displacement

V = [itex]\frac{dx}{dt}[/itex]

[itex]\int[/itex]2.10t dt=[itex]\int[/itex] dx

--integrating this this

1.05t2 = x

-- substituting 50m to x

t2 = 50/1.05
t= 6.9 seconds

For b.)

Doing the same for finding the velocity of the truck above i would get

3.4t = V (for the car)

Also by computing

[itex]\int[/itex]3.4t dt = [itex]\int[/itex]dx

I would get

1.7t2 = x

Substituting 6.9 seconds would result to
x = 80.94 m

subtract this from 50m the

80.94 - 50 = 30.94m

Is this correct? Thanks in advanced :D
 
Physics news on Phys.org
  • #2
Looks good to me!
 
  • #3
Whew, I was having doubts with my solution. Thanks!
 

What is the (Acceleration) Car and Truck Problem?

The (Acceleration) Car and Truck Problem is a common issue in which a car or truck experiences a delay in acceleration, resulting in slower speeds and potential safety hazards.

What causes the (Acceleration) Car and Truck Problem?

The (Acceleration) Car and Truck Problem can be caused by a variety of factors, including clogged fuel filters, faulty spark plugs, and transmission issues. In some cases, it may also be due to driver error or road conditions.

How can I diagnose the (Acceleration) Car and Truck Problem?

To diagnose the (Acceleration) Car and Truck Problem, you can start by checking the fuel system and spark plugs for any issues. You can also have a professional mechanic run a diagnostic test to pinpoint the exact cause of the problem.

How can I fix the (Acceleration) Car and Truck Problem?

The solution to the (Acceleration) Car and Truck Problem will depend on the underlying cause. In some cases, a simple tune-up or replacement of faulty parts may be enough to resolve the issue. However, more serious problems may require professional repairs or replacements.

How can I prevent the (Acceleration) Car and Truck Problem?

To prevent the (Acceleration) Car and Truck Problem, it is important to regularly maintain your vehicle and address any issues promptly. This includes regular oil changes, tune-ups, and inspections. It is also important to drive carefully and avoid harsh braking or accelerating, which can put unnecessary strain on your vehicle.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
836
  • Introductory Physics Homework Help
Replies
6
Views
590
  • Introductory Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Precalculus Mathematics Homework Help
Replies
4
Views
943
  • Introductory Physics Homework Help
Replies
25
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
11K
Back
Top