A jogger accelerates from rest to 5.64 m/s in 3.36 s. A car accelerates from 24.6 to 39.8 m/s also in 3.36 s. (a) Find the magnitude of the acceleration of the jogger. (b) Determine the magnitude of the acceleration of the car. (c) How much further does the car travel than the jogger during the 3.36 s?
a. a = (V-Vo)/t = (5.64-0)/3.36=1.68 m/s^2.
d1 = 0.5a*t^2 = 0.5*1.68*(3.36)^2=9.48 m.
b. a = (39.8-24.6)/3.36 = 4.52 m/s^2.
d2 = 0.5*4.52*(3.36)^2 = 25.5 m.
c. d2 d1 = 25.5 9.48 = 16.0 m.
c. d2-d1 = 25.5-9.48 = 16.0 m.
To find the magnitude of acceleration, you can use the equation:
acceleration = (final velocity - initial velocity) / time
(a) For the jogger:
The initial velocity of the jogger is 0 m/s (because they start from rest), the final velocity is 5.64 m/s, and the time taken is 3.36 s. Plugging these values into the acceleration formula:
acceleration = (5.64 m/s - 0 m/s) / 3.36 s
acceleration = 1.68 m/s²
So, the magnitude of the acceleration of the jogger is 1.68 m/s².
(b) For the car:
The initial velocity of the car is 24.6 m/s, the final velocity is 39.8 m/s, and the time taken is 3.36 s. Plugging these values into the acceleration formula:
acceleration = (39.8 m/s - 24.6 m/s) / 3.36 s
acceleration = 4.49 m/s²
So, the magnitude of the acceleration of the car is 4.49 m/s².
(c) To find how much further the car travels than the jogger during the 3.36 s, we need to calculate the distance covered by both.
For the jogger:
The distance covered by the jogger can be calculated using the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time²)
distance = (0 m/s * 3.36 s) + (0.5 * 1.68 m/s² * (3.36 s)²)
distance = 2.83 m
For the car:
The distance covered by the car can be calculated using the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time²)
distance = (24.6 m/s * 3.36 s) + (0.5 * 4.49 m/s² * (3.36 s)²)
distance = 176.93 m
The car travels 176.93 m - 2.83 m = 174.1 m further than the jogger during the 3.36 s.