Question

A car is 500 m behind a bus. They start moving at the same time. The bus starts moving at a constant velocity of 5 m/s. The car starts at an initial velocity of 0 and has an acceleration of 0.5 m/s^2. Calculate the time taken by the car to overtake the bus.

Answer 1

The car will take approximately 44.7 seconds to overtake the bus.

Step-by-step explanation:

To calculate the time taken by the car to overtake the bus, we need to compare the distances and velocities of the two vehicles. Let's start by finding the time it takes for the bus to travel the distance that separates it from the car:

The bus is moving at a constant velocity of 5 m/s. The distance it needs to cover is 500 m. Using the formula distance = velocity * time, we can rearrange the equation to find time = distance / velocity. Plugging in the values, we get time = 500 m / 5 m/s = 100 s.

Now, let's find the time it takes for the car to cover the same distance:

The car starts at an initial velocity of 0 and has an acceleration of 0.5 m/s². We can use the equation distance = initial velocity * time + (1/2) * acceleration * time² to solve for time. Rearranging the equation, we get time = square root[(2 * distance) / acceleration]. Plugging in the values, we get time = square root[(2 * 500 m) / 0.5 m/s²] = square root[2000 s²] = 44.7 s.

Therefore, it will take the car approximately 44.7 seconds to overtake the bus.