Question:

A car is traveling with an initial velocity of 10 m/s and uniformly accelerating at a rate of 2 m/s² for a duration of 5 seconds. Calculate the final velocity of the car and the distance it travels during this time.

Answer:

To find the final velocity and distance traveled by the car, we can use the following equations of motion:

1. Final Velocity:

v = u + at

2. Distance:

s = ut + 1/2 at²

Given:

Initial velocity (u) = 10 m/s Acceleration (a) = 2 m/s² Duration (t) = 5 seconds

Substituting these values into the equations of motion:

Final Velocity:

v = u + at

v = 10 m/s + 2 m/s² * 5 s

v = 10 m/s + 10 m/s

v = 20 m/s

Therefore, the final velocity of the car is 20 m/s.

Distance:

s = ut + 1/2 at²

s = 10 m/s * 5 s + 1/2 * 2 m/s² * (5 s)²

s = 50 m + 1/2 * 2 m/s² * 25 s²

s = 50 m + 1 * 2 m/s² * 25 s²

s = 50 m + 50 m

s = 100 m

Therefore, the distance traveled by the car is 100 m.

Hence, the final velocity of the car is 20 m/s and it travels a distance of 100 m during this time.