Physics, acceleration question?

Question

Ok, I really dont see why am I having a problem with this, it's just a matter of putting two equations toghether, but I just cant get the same answer the book has. So:
When the light turns green a car starts accelerating at constant 6 m/s^2 and at the same instant a truck passes it traveling 21 m/s. After how long will the car pass the truck?
As far as I can see we set up two equations?

d(t) = V x t
d(c) = 1/2 a t^2

then we put them together? leaving us with:

21 m/s x t = 6 t^2

we use the quadratic formula to find what t is ?

t = 7 s

Now we can just plug it in

d(t) = V x t = 21m/s x 7 s = 147
d(c) = 1/2 a t^2 = 3 m/s^2 x 49 = 147

the answer works... but the book says the answer is 168 m? Is there a chance that they actually just messed up ?

Answer 1

RUDE_BOI PLEASE READ THIS ANSWER BECAUSE I CHANGED IT!


I am leaving my previous stuff below so that other people can read them too.

The question asks, when the car will "pass" the truck. It does not ask when it will catch up. So it is just a word-play. At 7 s, the car has caught up with the truck, but has not passed it yet. Since you have a multiple choice question, you have to choose 168 m.

I hope you will select my answer as the best answer now, since I, too, have been struggling with this question for hours now :))

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(Here is my old answer)

Your calculations are correct, probably the book messed up.

I would like to point out that in your calculations above, you had a little typo:

" ... 21 m/s x t = 6 t^2 ..."

It should have been:

21 m/s x t = 1/2 x 6 x t^2 (or 21 m/s x t = 3 t^2)

But you did not carry over this typo further into the calculations and your calculations are correct.

The difference between 147 m and 168 m is 21 m, which is the speed of the truck per second. In other words, there seems to be an additional 1 s in the book's answer. Instead of 7 s, they seem to have put 8 s as the answer.

Most probably, initially the question was prepared as the car starting to accelerate 1 s after the truck passes by it - assuming 8 s would be the answer. But later they realized in 8 s, the car would be ahead of the truck. And they had to change the question, etc.

Bottom line ... your calculations are correct. Looks like the question was changed but they forgot to change the answer too.

Answer 2

You got it right. Not much point in me doing it again because you have already shown your complete working.

I'll just show that the book's answer is wrong.

The truck takes 8s to cover 168m --- 168/21=8

In 8 seconds the car has covered (1/2)*6*8^2 = 192m

After 8 seconds the car is 24m ahead of the truck.

Answer 3

Your answer seems correct but after 7 seconds, the car will be travelling at 176.4kph. Is there any other information in the question you are missing?

Answer 4

Yep.

Answer 5

YOUR RIGHT.... THERES PROBABLY A MESS UP IN THE BOOK.

Answer 6

why not b straight forward.ur talkin about distance when u meant time. may b am not getin u well....................