Final answer:
Using the kinematic equation v^2 = u^2 + 2as, with given initial velocity (3 m/s), acceleration (5 m/s^2), and distance (46 m), we calculate the final velocity to be approximately 21.66 m/s after the car accelerates for 46 meters.
Step-by-step explanation:
To solve for the final velocity of the car, we can use the kinematic equation that relates initial velocity, acceleration, and distance traveled without needing time. The formula is:
v2 = u2 + 2as
Where:
v is the final velocity,
u is the initial velocity,
a is the acceleration,
s is the distance travelled.
Given the initial velocity u = 3 m/s, acceleration a = 5 m/s2, and distance s = 46 m, we can plug these into the formula:
v2 = 32 + 2(5)(46)
Now solving for v2, we get:
v2 = 9 + 460
v2 = 469
To find v, we take the square root of both sides:
v = sqrt(469)
The final velocity v is approximately 21.66 m/s (after rounding the square root of 469). The car's final velocity is 21.66 m/s after accelerating for a distance of 46 meters.