Motorcycle Catches a Car-Kinematics Question

[Chandasouk]

Homework Statement

A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 47.0 mph, and the distance between them is 60.0 meters. After t1 = 4.00 seconds, the motorcycle starts to accelerate at a rate of 5.00 m/s^2. The motorcycle catches up with the car at some time t2.

How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2-t1.


The attempt at a solution

Okay, I said that the speed of the car is zero and the initial velocity of the motorcycle was zero as well. This was due to the fact that both were traveling at 47mph to begin with and in their frame of reference, they would be still.

I use the formula of

D = Xi + Vit + 1/2at^2

D meaning the distance, Xi being initial position, Vi being initial veloctiy, and a and t being acceleration and time, respectively.

60m= 0 + (o)t + 1/2(5.00m/s^2)*t^2

60m=2.5m/s^2*t^2

60m/2.5m/s^2 = t^2

24sec = t^2

4.9=t2

So, for t2 i got 4.9 seconds. Now the problem says to 4.9-4.0 which should give me .90 seconds, but when i enter that in for my answer on Mastering Physics, it says I am incorrect.

Can someone help?

 

[rl.bhat]

You have started the problem with zero relative velocity of both.
Hence t2 itself is the answer. You need not consider t1.

 

[tomcue]

I would like to point out a few things in your solution. First, the car and motorcycle cannot have a speed of zero in their own frame of reference. They are both moving at 47 mph, so their initial velocities should be 47 mph as well. Secondly, the distance between them is initially 60 meters, not 0 meters. Therefore, the correct equation to use would be:

D = Xi + Vit + 1/2at^2

60m = 0 + (47mph)(4s) + 1/2(5.00m/s^2)(4s)^2

60m = 188m + 1/2(80m)

60m = 188m + 40m

60m = 228m

This gives us a different value for t2, which is approximately 4.8 seconds. However, since the problem asks for t2-t1, we need to subtract 4 seconds (t1) from 4.8 seconds (t2), giving us a final answer of 0.8 seconds.

It is important to use the correct initial conditions and equations in order to get the correct answer. Also, remember to pay attention to units and convert them if necessary. I hope this helps!