Question

A taxi having a constant speed of 20 m/s is moving towards a stationary bus. If the bus increases its speed by a uniform acceleration of 2 m/s^2 while it was 100 m away from the taxi, calculate the time the taxi needs to catch the bus.

Answer 1

To calculate the time the taxi needs to catch the bus, we can calculate the time it takes for the bus to travel 100 m and the time it takes for the taxi to travel the same distance at its constant speed. It takes the bus 5 seconds to travel 100 m and the taxi also needs 5 seconds to catch the bus.

Step-by-step explanation:

To calculate the time the taxi needs to catch the bus, we need to determine the time it takes for the bus to travel the initial 100 m and then the time it takes for the taxi to travel the same distance at its constant speed. Let's start by calculating the time it takes for the bus to travel 100 m. We can use the equation:

s = ut + 0.5at^2

where s is the distance, u is the initial velocity, a is the acceleration, and t is the time. Plugging in the values, we have:

100 = 0 + 0.5(2)(t^2)

Simplifying this equation, we get:

t^2 = 100/2

t = 5 s

So, it takes the bus 5 seconds to travel 100 m. Now, let's calculate the time it takes for the taxi to travel 100 m at its constant speed:

s = ut

100 = 20t

Simplifying this equation, we get:

t = 5 s

Therefore, the taxi needs 5 seconds to catch the bus.