Calculating Time and Distance for a Tram with Sinusoidal Velocity

[ashclouded]

Homework Statement

The velocity of a tram traveling on a straight line between two stops is given by:
v = 16sin(pi(t)/30) m/s

find the time lapse between stops
the distance traveled between stops
the maximum velocity of the tram and when it occurs

Homework Equations

Displacement = x
Velocity = dx/dt
acceleration = dv/dt

The Attempt at a Solution

I don't have a clue how to start it

 

[putongren]

Hey,

You would want to know at what time the tram stopped. At what value would you equate v if you want to know when it stopped after it started? Since this equation is a sine wave, you know that the velocity oscillates. What is the relationship between displacement and velocity according to calculus. You were given an equation for velocity, then how do you find displacement from there?

 

[ashclouded]

Displacement is the antiderivative of velocity so I can find the intergral of the given equation, I'm still not sure about the first question on finding the time it stopped

 

[putongren]

Since you want to find the displacement, you want to find the integral of the velocity expression. I understand that's what you already know. The integral has two defining values when calculating it: beginning (start) and the end (finish). The time velocity begins and the time velocity stops. At what speed does v equal when velocity suddenly stops. Put it another way, when an object stops, what does the value v equate to. This should be the value of the upper value of the integral.

I'm not sure if I explained it clearly.

 

[ashclouded]

v will = 0 at rest, but if the initial velocity is also 0 and final velocity is 0 also then I don't know how I can get the desired answer if that made sense

 

[putongren]

The distance is just the integral from start to finish. When you find the value of the time when v = 0, then you can calculate the integral between the start and when the tram stops.