Question

A remote-control car is participating in a race. It speeds up from rest to 0.5 m/s in the distance of 2 meters. It then continues at a constant speed until it reaches the finish line. How long does it take for it to reach the finish line? If the race track is 15 meters long.

Answer 1

To find the time for the remote-control car to reach the finish line, calculate the time taken to accelerate to 0.5 m/s over 2 meters, and then add the time taken to travel the remaining distance at a constant speed of 0.5 m/s.

Step-by-step explanation:

To calculate the time it takes for the remote-control car to reach the finish line, we need to consider two parts of its journey. First, we need to find out how long it takes to accelerate from rest to 0.5 m/s, and then how much time it takes to cover the remaining distance at a constant speed.

For the acceleration part, we can use the formula for acceleration, which is final velocity (v) = initial velocity (u) + acceleration (a) × time (t). Since the car is accelerating from rest, the initial velocity (u) is 0. Given that the final velocity (v) is 0.5 m/s and the distance (s) covered during acceleration is 2 meters, we can also use the formula s = ut + (1/2)at^2 to calculate the time taken to accelerate.

For the constant speed part, the car travels the remaining distance (which is the total track length minus the distance covered during acceleration) at the constant speed of 0.5 m/s. We can use the formula time (t) = distance (s) / velocity (v) to find the time taken for this part of the journey. Finally, by adding the two times together, we get the total time to reach the finish line.