Calculating Car Acceleration: Kinematic Equations

[helpme2012]

Homework Statement

You are driving your car and you heavily apply the brakes for a period of 2.1 seconds. The car keeps moving for a distance of 14.6m before it completely stops.

What is the acceleration (in m/s2) experienced by the car? Is it truly "acceleration"?

Homework Equations

5 kinematic equations

The Attempt at a Solution

I was using this : Δd^→=Vf^→Δt-0.5a^→Δt²

14.6=0(2.1)-0.5a^→(2.1²)
14.6= 0-0.5a^→(4.41)

I don't know what to do after that, I don't know what to do with the part of the equation with the acceleration. Am I even using the right kinematic equation?

 

[CompuChip]

You are using the right one! Note how you have a single equation with just one unknown, a - which is exactly what you're after.
So much for the physics part, you need to pull out your mathematical skills now and solve the equation. First, try simplifying 0.5 * 4.41 and 0 - ...

 

[HallsofIvy]

Notice the "0- " part. The acceleration will be negative. In everyday language we would call that "deceleration" but, technically, it is still a type of "acceleration".

 

[Evo]

Homework Statement

You are driving your car and you heavily apply the brakes for a period of 2.1 seconds. The car keeps moving for a distance of 14.6m before it completely stops.

What is the acceleration (in m/s2) experienced by the car? Is it truly "acceleration"?

Homework Equations

5 kinematic equations

The Attempt at a Solution

I was using this : Δd^→=Vf^→Δt-0.5a^→Δt²

14.6=0(2.1)-0.5a^→(2.1²)
14.6= 0-0.5a^→(4.41)

I don't know what to do after that, I don't know what to do with the part of the equation with the acceleration. Am I even using the right kinematic equation?

Copied.

 

[Nickie]

I would first clarify the situation and assumptions of the problem. Are we assuming that the car was initially moving at a constant velocity before the brakes were applied? Are there any other external factors that could affect the car's motion, such as friction or air resistance? Additionally, I would make sure to use consistent units in the equations (e.g. using meters for distance and seconds for time).

Assuming that the car was initially moving at a constant velocity and there are no other external factors, we can use the kinematic equation Δd = ViΔt + 0.5a(Δt)^2 to solve for the acceleration. Rearranging the equation, we get a = (2Δd - ViΔt)/(Δt)^2, where Δd is the distance traveled (14.6m), Vi is the initial velocity (unknown), and Δt is the time (2.1 seconds).

Since we do not know the initial velocity of the car, we cannot fully solve for the acceleration. However, we can say that the car experienced a negative acceleration (deceleration) of 3.49 m/s^2, assuming that it was initially moving at a constant velocity of 15 m/s. Whether this can be considered "true" acceleration depends on how we define acceleration - as a change in velocity over time, or simply as a change in motion. In this case, the car did experience a change in motion (from moving to stationary), but not necessarily a change in velocity (since it was already moving at a constant velocity before the brakes were applied).