Calculating Time and Velocity for a Car Starting from Rest with Constant Acceleration

When a car starts from rest and accelerates at a constant rate, understanding its motion can be crucial for both practical applications and theoretical knowledge. Given a car accelerating at 4 m/s2 through a distance of 20 meters, we can calculate both the time it takes to cover this distance and its final velocity using kinematic equations.

Using Kinematic Equations

To solve for the time t without knowing the final velocity v, we can use the kinematic equation that relates distance s, initial velocity u, acceleration a, and time t:

s ut (1/2)at2

Given:

Plugging these values into the equation, we get:

20 0 * t (1/2) * 4 * t2

This simplifies to:

20 2t2

Dividing both sides by 2:

10 t2

Taking the square root of both sides:

t √10 ≈ 3.16 seconds

Calculating Final Velocity

To find the final velocity v of the car after it has traveled 20 meters, we can use the equation that relates v, u, a, and t:

v at

We already calculated t √10 ≈ 3.16 seconds. Substituting the values, we get:

v 4 * √10 ≈ 12.6 m/s

Additional Considerations

Various factors can affect the performance of a car, such as the type of tires and the overall weight of the vehicle. These factors can influence the actual acceleration and travel time. Tires, for instance, play a crucial role in the car's ability to generate traction and accelerate effectively. Weight can impact the car's inertia and overall performance.

For more accurate performance data, consider the specific details of the vehicle and its testing conditions. For homework, consider these factors as they can greatly affect the performance metrics of a car.

Using the kinematic equations, we can solve for the time and velocity of a car starting from rest with a given acceleration. The equations provide a clear and concise method for understanding the motion of the vehicle, even with limited information.