Simple Mechanics Problem

DaveRobinsonUK · 2010-09-20 20:11:52

Forgive me father, it has been 2 weeks since my last confession. I've been prepping for an interview. (no excuse i know )

I have started mechanics and so far so good, until I came across this one. It's had me stumped for a week now, probably simple I just can't see it.

o.k

The V-T graph shows the motion of a car and a bike as they travel along a straight road.
When t=0, the car and the bike pass a traffic light on the road.
At the traffic light the bike is travelling at 5ms-1 and the car is doing 3ms-1 and accelerating.

a) Explain how the graph indicates that the acceleration of the car is constant.
b) Find the acceleration of the car.
c) When t=T the car has travelled twice the distance of the bike. Find the value of T.

I can do a) and b) no problem, it's c that has me stumped and the more things I try the more confused I am getting about it.

Thanks guys.
Dave

mathsyperson · 2010-09-22 06:35:08

You need to find expressions for the distance travelled by the car and the bike at a certain time.

This is easy enough for the bike - it's travelling at a constant 5 m/s, so after t seconds it will have travelled a distance of 5t metres.

For the car it's a little trickier, but still not too bad. It's accelerating constantly, so its average speed between 0 and t seconds is its speed at (t/2) seconds. Use that average speed to work out the distance covered in the same way as was done for the bike.

Once you've got the two expressions, you just double the one for the bike, equate them and solve for t.

(Also, if you prefer, you can find distances travelled by looking at your V-T graph. The distance travelled by a vehicle in t seconds is the same as the area under that vehicle's line between 0 and t.)

George,Y · 2010-09-23 14:39:24

S=t*(v0+vt)/2=t*(v0+v0+a*t)/2=v0*t+a*t*t/2

DaveRobinsonUK · 2010-10-02 21:55:35

Hi guys

Sorry for the delay in reply again. I did get it on wednesday, seems so silly now.

I'm liking Mechanics, it gives you real examples and uses for all the Pure stuff I have and am learning.

Here was my solution

then :

so

then :

This is the answer given in the book, so I assume it is correct. Though it would be nice to have some
confirmation from the guys.

Thanks for all the help

Dave

Math Is Fun Forum

#1 2010-09-20 20:11:52

Simple Mechanics Problem

#2 2010-09-22 06:35:08

Re: Simple Mechanics Problem

#3 2010-09-23 14:39:24

Re: Simple Mechanics Problem

#4 2010-10-02 21:55:35

Re: Simple Mechanics Problem

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