Final answer:
The car's final velocity after merging is calculated using the uniform acceleration formula. With an initial velocity of 10.0 m/s and acceleration of 4.50 m/s² for 3.50 s, the final velocity is approximately 25.8 m/s, which corresponds to answer option C.
Step-by-step explanation:
The final velocity of the car after merging onto the highway can be calculated using the formula for uniform acceleration, which is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. The car starts with an initial velocity u of 10.0 m/s, accelerates at 4.50 m/s² for a time t of 3.50 s.
To find the final velocity, we plug these values into the formula:
v = u + at
v = 10.0 m/s + (4.50 m/s² × 3.50 s)
v = 10.0 m/s + 15.75 m/s
v = 25.75 m/s
The closest answer to 25.75 m/s is 25.8 m/s, which is option C.