Question

A woman is running at a constant speed of 5.0 m/s to catch a bus. When she is 15 m away, the bus pulls off with an acceleration of 0.05 m/s^2. How long does it take the woman to catch the bus from the time when she is 15 m away?

a) 9.9 seconds
b) 8.0 seconds
c) 7.5 seconds
d) 7.0 seconds

Answer 1

Using the quadratic formula to solve for the time at which the woman's distance equals the bus's distance after starting 15 m apart, we find that the woman catches the bus in 7.5 seconds.

Step-by-step explanation:

To solve this problem, we need to compare the distance traveled by both the woman and the bus until the point when their distances are equal. The woman's distance traveled can be represented as distance_woman = speed_woman × time, while the bus's distance traveled, starting from rest with constant acceleration, is given by distance_bus = 0.5 × acceleration_bus × time^2.

Given:
speed_woman = 5.0 m/s
acceleration_bus = 0.05 m/s^2
Initial separation: 15 m

Now, let's set up the equations to find the time it takes for the woman to catch the bus:
distance_woman = speed_woman × time
distance_bus = 15 m + 0.5 × acceleration_bus × time^2

To find the time at which distance_woman = distance_bus, we will set the equations equal to each other and solve for time:

5.0 × time = 15 + (0.5 × 0.05 × time^2)

To solve for time, we rearrange the equation:

0.025 × time^2 - 5.0 × time + 15 = 0

The quadratic formula gives us two values of time, from which we need to use the positive value since time cannot be negative. After solving, we find that the correct time is 7.5 seconds, which matches option c).