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 acceleration during the first 12 seconds of motion in m/s^2
To determine the car's acceleration during the first 12 seconds of motion, we can use the equation:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 30 m/s
Time (t) = 12 s
To find the final velocity (v) during this time, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Plugging in the values, we have:
750 m = (30 m/s * 12 s) + (0.5 * acceleration * (12 s)^2)
Simplifying the equation further, we get:
750 m = 360 m + 72 acceleration
Subtracting 360 m from both sides, we have:
390 m = 72 acceleration
Finally, solving for acceleration, we get:
acceleration = 390 m / 72
acceleration ≈ 5.42 m/s^2
Therefore, the car's acceleration during the first 12 seconds of motion is approximately 5.42 m/s^2.