Year 12s: what will be the first way you research your future options? >>

M1 graph question

For the first part, I see they intersect which is when they have the same speed , but I'm not too sure on how I'm meant to find it ?

For part 2, B will overtake A when they have travelled the same distance, so I found the area for A during the first 20seconds and for B. But don't know what to do further :confused:

(edited 11 years ago)

Reply 1

Implication

Original post by Tulian

For the first part, I see they intersect which is when they have the same speed , but I'm not too sure on how I'm meant to find it ?

One way would be to find the equation of the line for B between t=0 and t=20 and find where it intersects the line for A (v=8). Or you could work out the acceleration of B between t=0 and t=20 and use the definition of acceleration to work out at what time the speed will be 8ms^-1... I think that's actually the same method but with two different ways of thinking about it.

Original post by Tulian

For part 2, B will overtake A when they have travelled the same distance, so I found the area for A during the first 20seconds and for B. But don't know what to do further :confused:

Try finding the distance travelled by A - which'll be the distance travelled by A between t=0 and t=20 + the distance travelled by A between t=20 and t=T. Then try finding the value of T for whiuch the distance travelled by A is equal to the distance travelled by B. Should do the trick.

Reply 2

the bear

the overtaking is after 20 seconds. At 20 seconds A has done 160m whilst B has only done 140m.
After 20 seconds they are both travelling at a constant speed so you could model it by letting the slower one A stop and let the faster one B continue at the difference of their speeds until he has made up the 20m gap.