A truck traveling at a constant speed of 30.6 m/s passes by a police car which is at rest. The police officer catches up to the truck in 700 m, maintaining a constant
acceleration.
i)Calculate how long it took the police's car to overtake the truck speeder
To calculate the time it took for the police car to overtake the speeding truck, we need to use the equation of motion for the police car:
Distance = Initial velocity × Time + (1/2) × Acceleration × Time²
Given that the truck is traveling at a constant speed of 30.6 m/s and the police car is initially at rest, their initial velocities can be considered as 30.6 m/s and 0 m/s, respectively. The distance traveled by the police car to overtake the truck is 700 m.
Plugging in these values into the equation, we get:
700 m = 0 m/s × T + (1/2) × Acceleration × T²
Since the acceleration is constant, we can simplify the equation to:
700 m = (1/2) × Acceleration × T²
Now, we need to solve for T, which is the time it took for the police car to catch up to the truck.
Rearranging the equation, we have:
T² = (2 × 700 m) / Acceleration
T² = 1400 m / Acceleration
Taking the square root of both sides, we get:
T = √(1400 m / Acceleration)
Since the acceleration is not given in the question, we cannot calculate the exact time it took for the police car to overtake the truck without that information.