Question

You wish to exit the freeway at this exit. The exit speed shown on the sign is the speed at which you should:

1. Slow to before leaving the freeway.
2. Slow to while on the freeway exit ramp.
3. Never go slower than this speed on the exit ramp.
4. Never go faster than this speed anywhere on the exit ramp.

Answer 1

Using kinematic equations with the known initial velocity, acceleration, and time, we calculate that the car travels 172.8 meters in 12 seconds and reaches a final velocity of 28.8 m/s, which are reasonable figures for entering a freeway.

Step-by-step explanation:

Acceleration and Distance Calculation

To calculate the distance a car travels while entering a freeway from a standstill with a constant acceleration, you need to use kinematic equations. The acceleration equation is v = u + at, where 'v' is the final velocity, 'u' is the initial velocity (which is zero in this case), 'a' is the acceleration, and 't' is the time. For the distance, we use s = ut + 1/2at2.

In this scenario:

• Initial velocity (u) = 0 m/s
• Acceleration (a) = 2.40 m/s2
• Time (t) = 12.0 s

To find the distance:

1. Identify the unknown: Distance (s)
2. Select the appropriate equation: s = ut + 1/2at2
3. Solve for 's': s = 0 m/s * 12.0 s + 1/2 * 2.40 m/s2 * (12.0 s)2 = 0 + 0.5 * 2.40 * 144 = 172.8 meters

Thus, the car travels 172.8 meters in those 12 seconds. Units have been checked and the answer is reasonable for a typical freeway on-ramp.

To find the car's final velocity:

1. Using the equation v = u + at: v = 0 m/s + 2.40 m/s2 * 12.0 s
2. Calculate: v = 28.8 m/s

The car's final velocity after 12.0 seconds is 28.8 m/s. Again, units are consistent and the result is reasonable.