You are driving your car, and the traffic light ahead turns red. You apply the brakes for 2.28 s, and the velocity of the car decreases to + 4.76 m/s. The car’s deceleration has a magnitude of 2.99 m/s2 during this time. What is the car’s displacement?
vf^2=vi^2+2ad
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To find the car's displacement, we can use the equations of motion. Displacement (d) can be calculated using the formula:
d = (v_f^2 - v_i^2) / (2 * a)
Where:
- v_f is the final velocity (4.76 m/s in this case)
- v_i is the initial velocity (which we can assume to be 0 m/s since the car is at rest initially)
- a is the acceleration or deceleration (-2.99 m/s^2 in this case)
Since we already have the values for v_f, v_i, and a, we can substitute them into the equation to find the displacement:
d = (4.76^2 - 0^2) / (2 * -2.99)
Now, let's calculate it:
d = (22.6576 - 0) / (-5.98)
d = 22.6576 / -5.98
d ≈ -3.79 meters
Therefore, the car's displacement is approximately -3.79 meters. The negative sign indicates that the car is moving in the opposite direction of its initial motion.