# Kinematics In One Dimension

## Homework Statement

Two motorcycles are traveling due east with different velocities.
Four seconds later, they have the same velocity.
During this 4s interval, motorcycle 1 has an average acceleration of 2.0 m/s(squared) due east, while motorcycle 2 has an average acceleration of 4.0 m/s(squared) due east.
By how much did the speeds differ at the beginning of the 4s interval, and which motorcycle was moving faster.

No clue

## The Attempt at a Solution

Motorcycle 1 acceleration = 2.0 m/s(squared
So, in 4s, the distance covered is 8 meters.

Motorcycle 2 acceleration = 4.0 m/s(squared)
So, in 4s, the distance covered is 16 meters.

They are both traveling at the same velocity after 4s, so, since motorcycle 2 sped up more to attain the new final velocity, then motorcycle 1 must have been going faster prior to 4s.
Correct?

Now, how do I find the initial velocities of each motorcycle?

## The Attempt at a Solution

kuruman
Homework Helper
Gold Member
Here is a clue: You need to list the relevant kinematic equations first. Most textbooks show four. Find what they are and use them as a starting point.

You also seem to confuse velocity with acceleration. When the motorcycle has an acceleration of 2 m/s(squared) this means that for every second that goes by, 2 m/s are added to the velocity that is already there. So if at 1 s the velocity is 3 m/s, in 2 s the velocity will be 5 m/s and so on. What I just said is all you need to solve this problem. Find the kinematic equation that says the same thing symbolically and do a bit of algebra.

Another clue:

"By how much did the speeds differ at the beginning of the 4s interval..."

You are asked to find the difference in initial speeds, not necessarily what the speed of each motorcycle actually is. Mathematically, you are looking for the quantity:

difference in initial speed = Speed of cycle 1 - Speed of cycle 2 = some number
The sign (positive or negative) of the number will tell you which motorcycle was initially faster.

Thank you. I understand that part now. The problem now is that I don't have a final velocity or a displacement so there's atleast 2 unknown variables in each equation.

You don't need displacement. From the problem statement, you know what the accelerations are and that you have to deal with velocities. You should have a kinematic equation that involves just velocities and accelerations (which you used in one of your other questions).

You will have to use that equation twice, one for motorcycle 1 and again for motorcycle two. Although you don't know the final velocity, you do know that they are the same for both motorcycles. That should allow you to equate the two equations. Now you have one equation, with the two initial velocites and some numbers. Since you only need the difference between the velocities, you can find that number.

So, the difference in initial velocities = 8m/s ?

kuruman