Velocity and Acceleration Equational Problem ( making sense)

[zippeh]

Homework Statement

A man is running at speed c (much less than the speed of light) to catch a bus already at a stop. At t=0, when he is a distance b from the door to the bus, the bus starts moving with the positive acceleration a. Use a coordinate system with x=0 at the door of the stopped bus.

Part A:
What is xman(t), the position of the man as a function of time?
Answer symbolically in terms of the variables b, c, and t.

Homework Equations

v(t) = V₀+at

The Attempt at a Solution

I know that I need to use this equation:

v(t) = V₀+at

But I am confused because the answer is: x_man(t) = -b+ct. This doesn't make sense to me because in order to use this equation, c would need to be the acceleration, not the velocity. I tried reviewing the book and it really doesn't help. I know that the mans speed is constant, but with an acceleration c, wouldn't his velocity increase in time?

Sorry if this is a simple question, I just am trying to understand the foundations so that I can better apply myself later in the course. Thank you for your time.

 

[Tanya Sharma]

Homework Statement

A man is running at speed c (much less than the speed of light) to catch a bus already at a stop. At t=0, when he is a distance b from the door to the bus, the bus starts moving with the positive acceleration a. Use a coordinate system with x=0 at the door of the stopped bus.

Part A:
What is xman(t), the position of the man as a function of time?
Answer symbolically in terms of the variables b, c, and t.

Homework Equations

v(t) = V₀+at

The Attempt at a Solution

I know that I need to use this equation:

v(t) = V₀+at

But I am confused because the answer is: x_man(t) = -b+ct. This doesn't make sense to me because in order to use this equation, c would need to be the acceleration, not the velocity. I tried reviewing the book and it really doesn't help. I know that the mans speed is constant, but with an acceleration c, wouldn't his velocity increase in time?

Sorry if this is a simple question, I just am trying to understand the foundations so that I can better apply myself later in the course. Thank you for your time.

Welcome to PF!

If you are asked to find displacement , why should you be using equation for finding velocity .

You need to use the equation x(t) = x₀ + ut+(1/2)at² .

Here x₀ = -b , u=c , a=0 .

Does that make sense ?

 

[zippeh]

Oh wow... thanks!

I was looking through the equations that I know, and I couldn't arrive at the answer with anything that I had (so I thought). I immediately looked for an equation that looked similar to the answer, which was what I gave above. Thanks for making it clear, I didn't really ever think to set accel. to 0, which was what was made me stuck. I appreciate you helping me! :)

 

[Tanya Sharma]

You are welcome :)

 

[HalfLostAndSearching]

You are correct in your confusion. The given answer, xman(t) = -b+ct, does not make sense. In order to use the equation v(t) = V0+at, c would need to be the acceleration, not the velocity. It is likely a typo or error in the problem. The correct answer should be xman(t) = b+ct, where b is the initial distance between the man and the door of the bus and c is the constant speed of the man.

To further explain, the equation v(t) = V0+at is used to calculate the velocity at a given time t, given an initial velocity V0 and a constant acceleration a. In this problem, the man's velocity is constant, so the equation would not be used to find his position as a function of time.

Instead, we can use the equation x(t) = x0+V0t+1/2at^2, where x0 is the initial position, V0 is the initial velocity, and a is the constant acceleration. In this case, x0 = b, V0 = c, and a = 0 (since the man's velocity is constant). Plugging in these values, we get x(t) = b+ct, which is the correct answer.

It's important to always check the equations and units when solving problems to make sure they make sense and are used correctly. Good job on catching the error and seeking clarification. Keep up the good work!