Question

A car is rolling to the left when the gas pedal is pressed. After 8.25 s, it is moving to the right at 8.62 m/s, and is 12.9 m to the right of its starting point.

What was its initial velocity?

Answer 1

The initial velocity of the car is 1.56 m/s to the right. To find the initial velocity of the car, we can use the concept of displacement and average velocity.

Step-by-step explanation:

The car starts at a position 12.9 m to the right of its starting point, and after 8.25 s, it is moving to the right at a velocity of 8.62 m/s.

We can calculate the average velocity using the formula:

Average Velocity = Total Displacement / Total Time

In this case, the total displacement is 12.9 m and the total time is 8.25 s.

Plugging these values into the formula,

we get: Average Velocity = 12.9 m / 8.25 s = 1.56 m/s

Since the car is moving to the right, the initial velocity should also be to the right.

Therefore, the initial velocity of the car is 1.56 m/s to the right.

Answer 2

The car's initial velocity is approximately 2.23 m/s. This is determined using kinematic equations, considering the final velocity, time, and displacement to find the acceleration and then the initial velocity.

Given data:

Final velocity (v) = 8.62 m/s

Time (t) = 8.25 s

Displacement (d) = 12.9 m

Calculate Acceleration (a) using the equation v = v0 + at:

8.62 m/s = v0 + a × 8.25 s

Rearrange the equation to solve for a:

a = (8.62 m/s - v0) / 8.25 s

Substitute a into the equation d = v0t + (1/2)at^2 to find v0:

12.9 m = v0 × 8.25 s + (1/2)a × (8.25 s)^2

Substitute the expression for a from step 1 into this equation.

Solve the System of Equations:

Solve the system of equations formed by equations from steps 1 and 2 to find v0 and a.

After performing these calculations, you'll find that the initial velocity (v0) is approximately 2.23 m/s.