Final answer:
To determine the number of times the body traveled during the given time period, we need to find the distance traveled by the body. By using the equation v^2 = u^2 + 2as and the horizontal component of the force, we can calculate the distance traveled and divide it by the length of each travel. The body traveled approximately 124 times during that time period.
Step-by-step explanation:
To determine the number of times the body traveled during the time period, we need to find the distance traveled by the body. Since the body's speed increased from 10 m/s to 90 km/h, we need to convert the final speed to meters per second to maintain consistent units. 90 km/h is equal to 25 m/s.
Using the equation v^2 = u^2 + 2as, where v is the final speed, u is the initial speed, a is the acceleration, and s is the distance traveled, we can rearrange the equation to solve for s. Plugging in the values, we get 25^2 = 10^2 + 2(a)(s). Simplifying, we find that 625 = 100 + 2(a)(s). Solving for s, we get s = 262.5 m.
Since the body travels a distance of 262.5 m, we can divide this distance by the length of each travel to find the number of times the body traveled. The length of each travel is the horizontal component of the force, which can be found using the equation F_x = F * cos(theta), where F_x is the horizontal component of the force, F is the magnitude of the force, and theta is the angle of the force. Substituting the values, we get F_x = 3N * cos(45°) = 2.121 N. Dividing the total distance by the length of each travel, we get 262.5 m / 2.121 m per travel, which equals approximately 123.74. Therefore, the body traveled approximately 124 times during that time period.