Stationary motorcycle speeding up to a moving car

[aham925925]

Hi everyone

I was wondering if anybody knows how to do the questions that involve a moving car and a motorcycle speeding up from rest to overtake the car. The questions give you a velocity/time graph of the movement of both the car and the motorcycle to work with. the questions ask at what time does the motorcycle overtakes the car.

 

[rl.bhat]

Draw velocity/time graph of the movement of both the car and the motorcycle. If you find a point of intersection, then the motercycle overtakes the car and the point of intersection gives you the time.

 

[aham925925]

But wouldn't the intersection on a velocity/time graph be the point where both vehicles are moving at the same speed as opposed to being at an equal position from the start?

 

[cryptoguy]

i'd say integrate (find area under curve of) the V vs T graph to find D vs T, then see where their distances match up, and find the time when this occurs.

 

[rl.bhat]

When you start the clock, at t = 0, velocity of the motercycle will be zero and the car will have some velocity . They need not start from the same point but must be on the same line. To overtake the car motercycle must have larger acceleration. And they will meet when the realtive velocity of car and motercycle is zero.

 

[kplooksafterme]

If you haven't dealt with relative velocities yet (which I'm guessing you haven't) I'd approach the problem in lieu of kinematics. You can find the acceleration of each object (dv/dt) and the initial velocities from the individual graphs. Then just use your kinematic equations to find when (or where) the objects meet up.

 

[aham925925]

Do you know if there is a specific, more mathematical way of doing this sort of problem?

 

[rl.bhat]

Find the relative velocity of car and motercycle. (Vc - Vm) when t = 0. When motercycle ovetakes the car relative velocity = 0. To solve the problem you must know one more quantity, the acceleration of the motercycle.

 

[cristo]

If you haven't dealt with relative velocities yet (which I'm guessing you haven't) I'd approach the problem in lieu of kinematics. You can find the acceleration of each object (dv/dt) and the initial velocities from the individual graphs. Then just use your kinematic equations to find when (or where) the objects meet up.

Of course, this method will only work for uniform acceleration, which the OP does not specify.

 

[aham925925]

No, the graphs do not involves uniform accelerations.

The car is moving at the same velocity throughout and motorcycle accelerates from rest to a certain point, changes its acceleration and then travels at a constant velocity, which is higher that the car's.

 

[cryptoguy]

Yea I would suggest finding the area under the curve of both graphs (velocities of moto and car), and making a new D vs T graph. Plot both displacements on the same axis and see where they intersect.

 

[Feldoh]

Do you know if there is a specific, more mathematical way of doing this sort of problem?

Integrate the velocity functions of both the car and the motorcycle to get started.

 

[Petkovsky]

System of equations...