A speeder driving down the road at a constant 20m/s passes a patrolman parked on the roadside. The patrolman waits 3 seconds then pursue the speeder accelerating at a constant 4m/s2. When does the patrolman catch the speeder
7 seconds
To determine when the patrolman catches the speeder, we need to calculate the time it takes for the patrolman to catch up to the speeder.
Let's break down the problem step by step:
1. Calculate the distance the speeder travels during the 3-second delay of the patrolman:
- Distance = Speed × Time
- Distance = 20 m/s × 3 s
- Distance = 60 meters
2. Now, we need to find the time it takes for the patrolman to catch up to the speeder after the delay. We can use the equation of motion to calculate this.
- The equation of motion for distance traveled under constant acceleration is: Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
3. Let's assume the time it takes for the patrolman to catch the speeder is "t" seconds. The speeder is already 60 meters ahead of the patrolman at this point.
- For the patrolman: Distance = 0 meters (since he starts from rest)
- For the speeder: Distance = 60 meters (since he was already 60 meters ahead)
4. Applying the equation of motion to both the patrolman and the speeder:
- For the patrolman: 0 = 0 × t + 0.5 × 4 m/s^2 × t^2
- 0.5 × 4 m/s^2 × t^2 = 0
- t^2 = 0 / (0.5 × 4 m/s^2)
- t^2 = 0
5. Since the numerator is zero, the equation becomes: t^2 = 0. Dividing by zero is undefined, so we cannot directly solve for t using this equation.
6. However, common sense tells us that the patrolman can never catch the speeder if they both maintain constant velocities. This is because the speeder is driving faster and will continue to increase their distance from the patrolman.
Hence, the patrolman will never catch the speeder.