Question

A car traveling 56.0 km/h is 25.0 m from a haystack when the driver slams on the brakes. The car hits the haystack 2.11 s later. How fast is the car traveling at impact?

Answer 1

The speed of the car at impact is approximately 25.72 m/s.

Step-by-step explanation:

To find the speed of the car at impact, we first need to calculate the deceleration. We can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

Given that the initial velocity (u) is 56.0 km/h, the distance (s) is 25.0 m, and the time taken (t) is 2.11 s, we can rearrange the equation to solve for a: a = (v - u) / t.

Plugging in the values, we have a = (0 - 56.0 km/h) / 2.11 s = -26.5 m/s². Since the car is decelerating, the acceleration is negative.

Now, to find the final velocity (v) at impact, we can use the equation v² = u² + 2as. Rearranging the equation, we have v² = u² + 2(-26.5 m/s²)(25.0 m) = u² - 2(26.5 m/s²)(25.0 m).

Plugging in the values, we have v² = (56.0 km/h)² - 2(26.5 m/s²)(25.0 m).

Converting the initial velocity (u) to m/s, we get u = 56.0 km/h * (1000 m/1 km) * (1 h/3600 s) = 15.6 m/s.

Substituting the values, we have v² = (15.6 m/s)² - 2(26.5 m/s²)(25.0 m) = 0.16 m²/s² - 26.5 m²/s² * 25.0 m = 0.16 m²/s² - 662.5 m²/s² = -662.34 m²/s².

Taking the square root of both sides, we get v ≈ √(-662.34 m²/s²) ≈ -25.72 m/s.

Since speed is a positive quantity, the speed of the car at impact is approximately 25.72 m/s.

Answer 2

The car is traveling at
`8.1366(m)/(s)`

Step-by-step explanation:

The known variables are the following:

`V_(0) = 56 (km)/(h) = 15.56 (m)/(s)\\ D=25m\\ t=2.11s\\ V_(f)=?`

First, from the equation of motion we find the deceleration:

`D=V_(0)*t+(1)/(2) a*t^(2) \\ a=(2(D-V_(0)))/(t^(2) ) \\ a=3.5182(m)/(s^2)`

Then, with the equation for the speed:

`V_(f)=V_(o)+a*t\\ V_(f)=8.1366(m)/(s)`