At the local playground, a 21-kg child sits on the right end of a horizontal teeter-totter, 1.8 m from the pivot point. On the left side of the pivot an adult pushes straight down on the teeter-totter

(a) To find how far the car travels before overtaking the truck, we need to set up an equation for the distance traveled by each vehicle. Let t be the time it takes for the car to overtake the truck. Then: Distance traveled by car = initial distance + 1/2(at^2) Distance traveled by truck = (20.0 m/s)t Since they meet at the moment the car overtakes the truck, we can set these distances equal to each other and solve for t: initial distance + 1/2(at^2) = (20.0 m/s)t 0 + 1/2(3.20 m/s^2)(t^2) = (20.0 m/s)t 1.60t^2 = 20.0t t = 12.5 s Now we can plug this value of t back into either equation to find the distance traveled by the car: Distance traveled by car = initial distance + 1/2(at^2) = 0 + 1/2(3.20 m/s^2)(12.5 s)^2 = 250 m Therefore, the car overtakes the truck 250 m beyond its starting point. (b) To find the speed of the car when it overtakes the truck, we need to use the value of t we found in part (a) and the equation for velocity with constant acceleration: Final velocity = initial velocity + acceleration x time At the instant the traffic light turns green, the car has an initial velocity of 0. So: Final velocity of car = 0 + 3.20 m/s^2 x 12.5 s = 40.0 m/s Therefore, the car is traveling at 40.0 m/s when it overtakes the truck. (c) To sketch an x-t graph of the motion of both vehicles, we can use the equations for distance traveled we set up in part (a). The graph will show the position of each vehicle as a function of time. Here is a rough sketch: ^ 300 | 250 | ___////___ 200 | __/ 150 | / 100 |/ 50 | |___________________> Time (s) The sloping line represents the distance traveled by the truck, which increases at a constant rate of 20.0 m/s. The curve represents the distance traveled by the car, which starts at 0 and increases with a parabolic shape as the car accelerates. (d) To sketch a vx-t graph of the motion of both vehicles, we can use the equation for velocity we used in part (b). The graph will show the velocity of the car as a function of time. Since the truck has a constant velocity, its vx-t graph will be a horizontal line. Here is a rough sketch: ^ 50 | / __/ __ 40 | | |/ 30 | | 20 | | 10 |___________________ Time (s) The sloping line represents the velocity of the car, which starts at 0 and increases linearly with time as the car accelerates. The point where it intersects with the horizontal line representing the velocity of the truck is the moment when the car overtakes the truck. At this point, the velocity of the car jumps up to 40.0 m/s, which is the velocity of the truck.