Question

CAN Someone Please Help on this physics problem?

While driving at 27 m/s, the driver steps in the gas to beat a yellow light. They accelerate at 2.8 m/s^2. They drive through the intersection that is 55 m long. How fast were they going after going through the intersection? Remember to show work including know values, unknown values, equation used, plugging into equation and displayed answer with proper units.

Answer 1

the driver's speed after going through the intersection is approximately 32.2 m/s.

Step-by-step explanation:

To determine the speed of the driver after going through the intersection, we can use the kinematic equation:

v^2 = u^2 + 2as

Where: v = final velocity (unknown)

u = initial velocity = 27 m/s

a = acceleration = 2.8 m/s^2

s = distance traveled = 55 m

First, let's calculate the value of v^2: v^2 = (27 m/s)^2 + 2(2.8 m/s^2)(55 m)

v^2 = 729 m^2/s^2 + 2(2.8 m/s^2)(55 m)

v^2 = 729 m^2/s^2 + 308 m^2/s^2

v^2 = 1037 m^2/s^2

Now, let's find the square root of both sides to solve for v: v = √(1037 m^2/s^2)

v ≈ 32.2 m/s

Therefore, the driver's speed after going through the intersection is approximately 32.2 m/s.

Please note that rounding the final answer to two decimal places is a common practice, but you can use more decimal places if necessary.