Math Is Fun Forum

markosheehan

Member

Registered: 2016-06-15

Posts: 51

uniform acceleration

A car, starting from rest and travelling from p to q on a straight level road,
where | pq | = 10 000 m, reaches its maximum speed 25 m/s by constant
acceleration in the first 500 m and continues at this maximum speed for the
rest of the journey.
A second car, starting from rest and travelling from q to p, reaches the same
maximum speed by constant acceleration in the first 250 m and continues at
this maximum speed for the rest of the journey.
(i) If the two cars start at the same time, after how many seconds do the
two cars meet ?
Find, also, the distance travelled by each car in that time.

i am trying to use uvast equations to solve this but i cant. can someone help me

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: uniform acceleration

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: uniform acceleration

hi markosheehan

I find it is helpful to sketch a velocity / time graph for problems like this:

The area under the graph represents the distance travelled, so you can calculate the time indicated at the end of the shaded region.  I have shown the second car's velocity below the axis as it is travelling in the opposite direction.

EDIT

Once you know the two times at the start of maximum velocity, you can ignore the acceleration phase, and just do a straight line distance time graph for the two cars.  For clarity I have 'condensed' the distance between the two critical 'start' times.

Bob

Last edited by Bob (2016-09-10 20:56:46)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

markosheehan

Member

Registered: 2016-06-15

Posts: 51

Re: uniform acceleration

ok thanks for the graph and which uvast equation are you using thickhead.

Last edited by markosheehan (2016-09-10 22:54:39)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: uniform acceleration

hi markosheehan

For t1 and t2 you can use, a = v/t as it's constant.  You can see the same from the gradient on the V/T graph.

Then the velocity is constant, so you can use D = ST.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: uniform acceleration

ok thanks for the graph and which uvast equation are you using thickhead.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}