A car entering the freeway accelerates from 10.2 m/s with a constant acceleration of 4.4 m/s2. What is the car’s final velocity when it merges onto the highway and reaches its cruising speed 4.2 seconds later?
A
28.7 m/s
B
11.2 m/s
C
18.5 m/s
D
8.28 m/s
To find the car's final velocity, we can use the equation:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
u = 10.2 m/s (initial velocity)
a = 4.4 m/s^2 (acceleration)
t = 4.2 seconds (time)
By substituting the given values into the equation, we have:
v = 10.2 m/s + (4.4 m/s^2)(4.2 s)
v = 10.2 m/s + 18.48 m/s
v = 28.68 m/s
Thus, the car's final velocity when it merges onto the highway and reaches its cruising speed 4.2 seconds later is approximately 28.7 m/s.
Therefore, the correct answer is option A: 28.7 m/s.
To find the car's final velocity when it merges onto the highway, we can use the following equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
Initial velocity (u) = 10.2 m/s
Acceleration (a) = 4.4 m/s^2
Time (t) = 4.2 seconds
Plugging in the values into the equation, we have:
v = 10.2 m/s + (4.4 m/s^2)(4.2 s)
v = 10.2 m/s + 18.48 m/s
v = 28.68 m/s
Therefore, the car's final velocity when it merges onto the highway is approximately 28.7 m/s.
The correct answer is A.