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 :)