A car 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 calculate the acceleration of the car during the deceleration phase.
First, let's calculate the initial velocity of the car when it reaches the road sign. We know that the car covers a distance of 750 meters in a time of 12 seconds.
Using the formula:
v = d/t
v = 750m / 12s
v = 62.5 m/s
Therefore, the initial velocity of the car when it reaches the road sign is 62.5 m/s.
Next, let's calculate the acceleration of the car while it's decelerating from 62.5 m/s to 0 m/s.
Using the formula:
a = (vf - vi) / t
a = (0 m/s - 62.5 m/s) / (14s - 12s)
a = (-62.5 m/s) / 2s
a = -31.25 m/s²
Therefore, the acceleration of the car is -31.25 m/s².
Finally, let's calculate the final velocity of the car when t=14 seconds.
Using the formula:
vf = vi + a * t
vf = 62.5 m/s + (-31.25 m/s²) * 14s
vf = 62.5 m/s + (-437.5 m/s²)
vf = -375 m/s
Therefore, the car's velocity at t=14 seconds is -375 m/s. Note that the negative sign indicates that the car is moving in the opposite direction.