How Far Beyond Its Starting Point Does the Car Overtake the Truck?

January 2, 2024

At the instant the traffic light turns green, a car waiting at an intersection starts ahead moving with a constant acceleration of 2m/s2. At the same time a truck traveling with a constant speed of 10 m/s overtakes and passes the automobile. (a) How far beyond its starting point does the car overtake the truck? (b) How fast is the car travelling at that moment? Draw the position – time curves for each vehicle.

Answer: To find the distance the car will travel to overtake the truck, use the following formula: Distance_car = initial velocity * time + (1/2) * car’s acceleration * time. For the truck’s initial velocity, its equation simplifies to v = t. Hence, t = 12 m/s for the truck. Consequently, the distance the car will cover to overtake the truck is t = 100 meters.

The key to safely passing a truck is to maintain control of the car and follow proper passing procedures, such as signaling and checking blind spots. Moreover, it’s important to note that the size of a truck can also impact the passing process by creating larger blind spots for the driver of the passing car, which may require more time and distance to pass. As a result, it’s often beneficial to accelerate when possible to increase the speed of the vehicle and reduce the amount of time needed to overtake the truck. This way, the truck can be passed at a safer rate without risking the lives of drivers and passengers alike.


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