To solve this problem, we need to divide it into three parts: the acceleration phase, the constant velocity phase, and the deceleration phase. Let's calculate the time for each phase and then sum them up to find the total time.
- Acceleration Phase: Using the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given: Initial velocity (u) = 0 m/s Final velocity (v) = 20 m/s Acceleration (a) = 2.5 m/s²
Using v = u + at, we can rearrange the equation to solve for time (t): t = (v - u) / a
t = (20 - 0) / 2.5 = 8 seconds
- Constant Velocity Phase: The car travels at a constant velocity of 20 m/s, so the time taken in this phase is given by the total distance divided by the velocity:
Time = Distance / Velocity = 500 m / 20 m/s = 25 seconds
- Deceleration Phase: The car decelerates at a rate of 4 m/s² until it comes to a stop. The final velocity in this phase is 0 m/s. Using the same equation of motion:
Given: Initial velocity (u) = 20 m/s Final velocity (v) = 0 m/s Acceleration (a) = -4 m/s² (negative because it's deceleration)
t = (v - u) / a
t = (0 - 20) / (-4) = 5 seconds
Now, we can find the total time by adding up the times from each phase:
Total time = Acceleration time + Constant velocity time + Deceleration time = 8 seconds + 25 seconds + 5 seconds = 38 seconds
Therefore, it will take 38 seconds to cover the total distance of 500 meters.