Displacement given the acceleration

[Guillem_dlc]

Homework Statement

How could I get the distance traveled by a vehicle having only its constant acceleration as data?

Homework Equations

I know that the acceleration is the derivative of the velocity and the velocity is the derivative of the position.

The Attempt at a Solution

I don't know how to find the position because I have only the acceleration.

 

[Hydrous Caperilla]

use equations of kinematics

 

[Dr.D]

having only its constant acceleration as data?

You can safely assume that the initial displacement is zero from the way the question is framed.

Unfortuately, you cannot justifiably make such an assumption about the initial velocity. This leave the problem without a solution.

 

[Guillem_dlc]

At the instant when a traffic light turns green, a car starts to move with a constant acceleration of 3ms ^ 2, at that same moment, a motorcycle is placed at its speed at a constant speed of 20ms. The two vehicles continue advancing past the traffic light.

Calculate the distance, measured from the traffic light, which runs until it is at the height of the motorcycle

The speed of the car at the time it is at the height of the motorcycle

 

[Dr.D]

What you have just posted is not quite the problem in post #1.

which runs until it is at the height of the motorcycle

As it stands, this does not quite make sense. Are you sure that height is the word you want heree?

 

[Guillem_dlc]

What you have just posted is not quite the problem in post #1.
As it stands, this does not quite make sense. Are you sure that height is the word you want heree?

which runs until it is at the same distance of the motorcycle.

Thanks

 

[CWatters]

Homework Equations

I know that the acceleration is the derivative of the velocity and the velocity is the derivative of the position.

The Attempt at a Solution

I don't know how to find the position because I have only the acceleration

The opposite of differentiation is integration. You will need to think about the constants.

 

[Dr Dr news]

You need to specify the initial conditions of position and velocity to solve the problem. Then it is just an application of the 1D kinematic equation. x(t) = x(0) + v(0) t + a t^2 / 2.

 

[haruspex]

At the instant when a traffic light turns green, a car starts to move with a constant acceleration of 3ms ^ 2, at that same moment, a motorcycle is placed at its speed at a constant speed of 20ms. The two vehicles continue advancing past the traffic light.

Calculate the distance, measured from the traffic light, which runs until it is at the height of the motorcycle

The speed of the car at the time it is at the height of the motorcycle

Just to clean up the English a bit, I think you are saying that the car and motorcycle pass the traffic light at the same time, the car accelerating from rest at 3m/s² and the motorcycle moving at a constant 20 m/s.
Suppose they meet again time t later. How far has each gone?