Question

A heavy dump trunk approaches a stop sign with a speed of 15 m/s to the East. The dump truck decelerates uniformly coming to a stop. If the truck travels 160 m while decelerating, how much time does it take to come to rest while braking?

Answer 1

The dump truck takes 1 second to come to a stop while braking.

Step-by-step explanation:

To calculate the time it takes for the dump truck to come to a stop while braking, we can use the equation:

vf = vi + at

where:

vf is the final velocity (0 m/s)

vi is the initial velocity (15 m/s)

a is the acceleration (which is the deceleration in this case)

t is the time

The acceleration can be calculated using another equation:

a = (vf - vi) / t

where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.

Given that the truck travels 160 m while decelerating, we can plug in the values into the equation:

-15 m/s = (0 m/s - 15 m/s) / t

Simplifying the equation, we get:

-15 m/s = -15 m/s / t

Cross multiplying, we have:

-15 m/s * t = -15 m/s

Dividing both sides of the equation by -15 m/s, we find that:

t = 1 second

Therefore, it takes 1 second for the dump truck to come to rest while braking.