# How Does Velocity Impact Acceleration in Race Cars?

• MHB
• karush
In summary, a race car starts from rest and travels east along a straight and level track. For the first 5.0s of the car's motion, the eastward component of its velocity is given by $v_x(t) = (0.93 m/s^3)t^2$. The acceleration of the car when $v_x = 14.5$ is calculated to be 7.35 m/s^2.
karush
Gold Member
MHB
A race car strarts from rest and travels east along a straight and level track.
For the firs $5.0s$ of the cars motion,
the eastward compent of the car's velocity,is given by
$v_x(t)=(0.930 m/s^3)t^2$
What is acceleration of the car when $v_x=14.5$

ok my first step with this was

$$A=\frac{dv}{dt}=1.86t$$
if $v=14.5=0.933t^2$
then
$$t=3.94$$

so

$A(3.94)=1.86\cdot3.94=7.32 m/s^2$

Last edited:
You give, as the speed function, $$\displaystyle 0.930 t^2$$, but when calculating the time when the speed is 14.5, you have $$\displaystyle 0.933t^2$$. Which is correct, 0.930 or 0.933?

Hope this is better got lost in the W|A output

A race car strats from rest and travels east along a straight and level track.
For the first 5.0s of the cars motion,
the eastward compent of the car's velocity,is given by
$v_x(t)=(0.93 m/s^3)t^2$
a. What is acceleration of the car when \$v_x=14.5
\displaystyle \begin{align*} \displaystyle A&=\frac{dv}{dt}=1.86t\\ v&=14.5=0.93t^2\\ t&=3.94\\ A(3.94)&=1.86\cdot3.94=7.35 m/s^2 \end{align*}

I was ? on round off

## 1. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. In simpler terms, it is how quickly an object's speed is increasing or decreasing.

## 2. How is acceleration measured?

Acceleration is typically measured in meters per second squared (m/s^2) in the metric system, or feet per second squared (ft/s^2) in the imperial system. It can also be measured in other units such as kilometers per hour squared (km/h^2) or miles per hour squared (mph^2).

## 3. What factors affect the acceleration of a car?

The acceleration of a car can be affected by several factors, including the power of the engine, the weight and aerodynamics of the car, the type and quality of the tires, and the condition of the road.

## 4. How is acceleration related to force?

According to Newton's second law of motion, force is directly proportional to acceleration. This means that the greater the force applied to an object, the greater its acceleration will be.

## 5. How can acceleration be calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. This can be represented by the equation a = (vf - vi) / t, where a is acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken for the change in velocity to occur.

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