Isaac Physics: Will they collide

Does anyone know how to solve this?

A lorry travelling along a narrow road with speed u1 applies its brakes to give a uniform deceleration of magnitude a1. At the same time a car, a distance d behind the lorry and travelling in the same direction with speed u2, applies its brakes to give a uniform deceleration of magnitude a2.

Show that the car collides with the now stationary lorry if (a2) (ku2)^2, and find k in terms of u1, d and a1 .
(edited 4 months ago)
Original post by Ds.sd06
Does anyone know how to solve this?

A lorry travelling along a narrow road with speed u1 applies its brakes to give a uniform deceleration of magnitude a1. At the same time a car, a distance d behind the lorry and travelling in the same direction with speed u2, applies its brakes to give a uniform deceleration of magnitude a2.

Show that the car collides with the now stationary lorry if (a2) (ku2)^2, and find k in terms of u1, d and a1 .

For the two vehicles to collide, the displacement made by the lorry during the brake is equal to the displacement made by the car plus d.

The displacement of the lorry and car can be found using the suvat equations.
Original post by Eimmanuel
For the two vehicles to collide, the displacement made by the lorry during the brake is equal to the displacement made by the car plus d.

The displacement of the lorry and car can be found using the suvat equations.

Thank you, I’ll try it now
Original post by Eimmanuel
For the two vehicles to collide, the displacement made by the lorry during the brake is equal to the displacement made by the car plus d.

The displacement of the lorry and car can be found using the suvat equations.

I’m not sure how to do this, are you able to walk me through it?
Original post by Ds.sd06
I’m not sure how to do this, are you able to walk me through it?

Do you know the suvat equations?

If yes, which equation would you use to find the displacement based on the given info?
Original post by Eimmanuel
Do you know the suvat equations?

If yes, which equation would you use to find the displacement based on the given info?

I know them yes, none of the information have a numerical value though, however I would assume it’s
V^2 = U^2 + 2as rearranged to give S
Original post by Ds.sd06
I know them yes, none of the information have a numerical value though, however I would assume it’s
V^2 = U^2 + 2as rearranged to give S

Indeed, v2 = u2 + 2as should be chosen and rearrange to get s. Do this to find the displacement of car and lorry.
Then substitute into the following and make a2 the subject.
displacement of lorry (in term of a2 and u2) = d + displacement of car (in term of a1 and u1)
Original post by Eimmanuel
Indeed, v2 = u2 + 2as should be chosen and rearrange to get s. Do this to find the displacement of car and lorry.
Then substitute into the following and make a2 the subject.
displacement of lorry (in term of a2 and u2) = d + displacement of car (in term of a1 and u1)

I got this but it is incorrect
-u_2^2/2a_2 is equal to or less than -u_1^2/2a_1 + d
Ahh never mind I solved to get a_2 is less than or equal to 2u_1^2 - 2ad/2a_1u_2^2
(edited 4 months ago)
Original post by Ds.sd06
I got this but it is incorrect
-u_2^2/2a_2 is equal to or less than -u_1^2/2a_1 + d

Ignore the inequality first, your answer is correct but not in the correct form.
Remember you need to make a2 the subject or "isolate" a2 to the left-hand side but it needs to be in the numerator.
Original post by Eimmanuel
Ignore the inequality first, your answer is correct but not in the correct form.
Remember you need to make a2 the subject or "isolate" a2 to the left-hand side but it needs to be in the numerator.

How exactly would I do that?
Original post by Ds.sd06
How exactly would I do that?

Have a watch on this video.
Convert right-hand side terms into a single fraction and then cross-multiply to move a_2 to the right-hand side numerator.
Make a_2 the subject should be doable from here. If not post a picture of what you have done.
Original post by Eimmanuel
Have a watch on this video.
Convert right-hand side terms into a single fraction and then cross-multiply to move a_2 to the right-hand side numerator.
Make a_2 the subject should be doable from here. If not post a picture of what you have done.

How do I upload a photo?
(edited 4 months ago)

See the diagram above. Click on the camera icon and bring forth a window where it will allow you to choose the picture for you to upload.
Original post by Eimmanuel

See the diagram above. Click on the camera icon and bring forth a window where it will allow you to choose the picture for you to upload.

I don’t have this option available
Original post by Ds.sd06
I don’t have this option available

Are you using a phone or computer?
Original post by Eimmanuel
Are you using a phone or computer?

Phone but don’t worry I was able to solve it
Original post by Ds.sd06
Does anyone know how to solve this?

A lorry travelling along a narrow road with speed u1 applies its brakes to give a uniform deceleration of magnitude a1. At the same time a car, a distance d behind the lorry and travelling in the same direction with speed u2, applies its brakes to give a uniform deceleration of magnitude a2.

Show that the car collides with the now stationary lorry if (a2) (ku2)^2, and find k in terms of u1, d and a1 .