A car initially traveling at 30 m/s passes a road sign located 750 meters ahead in a time of 12 seconds. When the car reaches the road sign, the driver applies the brakes and brings the car to rest at a traffic light located 900 meters ahead of the road sign.
Determine the cars velocity in m/s at t=14 seconds
To determine the car's velocity at t=14 seconds, we need to consider its motion before and after reaching the road sign.
Before reaching the road sign, the car traveled a distance of 750 meters in 12 seconds. We can use the equation:
Distance = Velocity × Time
750 = Velocity × 12
Solving for velocity, we find:
Velocity = 750 / 12 = 62.5 m/s
So, before reaching the road sign, the car's velocity is 62.5 m/s.
After reaching the road sign, the car applies the brakes and comes to a stop at the traffic light located 900 meters ahead. This means the car travels an additional distance of 900 - 750 = 150 meters.
Since the car comes to a rest, its final velocity is 0 m/s. We can use the equation:
Final Velocity^2 = Initial Velocity^2 + 2 × Acceleration × Distance
Since the final velocity is 0 and we want to find the acceleration, the equation becomes:
0 = (62.5)^2 + 2 × Acceleration × 150
Solving for the acceleration, we find:
2 × Acceleration × 150 = - (62.5)^2
Acceleration = - (62.5)^2 / (2 × 150)
Acceleration ≈ -13.33 m/s^2
Now we can use the formula:
Velocity = Initial Velocity + Acceleration × Time
to find the car's velocity at t=14 seconds.
Velocity = 62.5 + (-13.33) × 14
Velocity ≈ 62.5 - 186.62
Velocity ≈ -124.12 m/s
Therefore, at t=14 seconds, the car's velocity is approximately -124.12 m/s.