Mechanics: Straight line motion

  • Thread starter MilenaMath
  • Start date
  • #1
1. A car is sitting at a stop light and then accelerates from rest when the light turns green.The acceleration of the car is a combination of forward acceleration but also slowing down due to drag forces.The final total accelaration of the car has the form a(t)=b/(t+T)^3 with constants b=2000 m s and T=10s
a) What are the cars velocity and position as a function of time?
b) What are the car's velocity and position at t=5.0 s?







Attempt to a solution. I calculated integral of the acceleration function and got v(t)=b/[-2*(t+T)^2] and x(t)=b/[2(t+T)] However it doesnt coincide with what the teacher has got in his answer.I got 4.44m/s and 66.6 m as answerst to b) part.Did I make a mistake anywhere,the problem must be trivial,but I am afraid I am doing something wrong.Can anyone help me please?
 

Answers and Replies

  • #2
Doc Al
Mentor
45,093
1,397
I calculated integral of the acceleration function and got v(t)=b/[-2*(t+T)^2]
What's the velocity at t = 0? (I think you forgot to consider the constant of integration.)
 
  • #3
True! then I get constant as b/[-2T^2]. Thank you! (Since car is initially at rest I assume v(0)=0)
 

Related Threads on Mechanics: Straight line motion

  • Last Post
Replies
11
Views
2K
Replies
11
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
2
Replies
26
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
10
Views
4K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
7
Views
4K
Top