To find the acceleration of an object, you can use the equation:
acceleration = (final velocity - initial velocity) / time
For the jogger:
(a) The jogger's initial velocity is 0 m/s (since the jogger starts from rest), the final velocity is 2.7 m/s, and the time is 2.2 s. Substituting these values into the equation:
acceleration = (2.7 m/s - 0 m/s) / 2.2 s = 1.227 m/s²
So, the magnitude of the jogger's acceleration is 1.227 m/s².
For the car:
(b) The car's initial velocity is 39.0 m/s, the final velocity is 44.0 m/s, and the time is 2.2 s. Substituting these values into the equation:
acceleration = (44.0 m/s - 39.0 m/s) / 2.2 s = 2.273 m/s²
So, the magnitude of the car's acceleration is 2.273 m/s².
To determine whether the car travels farther than the jogger during the 2.2 s, we need to compare their displacements. The displacement of an object with constant acceleration can be determined using the equation:
displacement = (initial velocity * time) + (0.5 * acceleration * time²)
For the jogger:
initial velocity = 0 m/s (since the jogger starts from rest)
displacement_jogger = (0 m/s * 2.2 s) + (0.5 * 1.227 m/s² * (2.2 s)²) = 2.692 m
For the car:
initial velocity = 39.0 m/s
displacement_car = (39.0 m/s * 2.2 s) + (0.5 * 2.273 m/s² * (2.2 s)²) = 99.42 m
Since the displacement of the car (99.42 m) is greater than the displacement of the jogger (2.692 m), the car travels farther than the jogger during the 2.2 s.