Question

Unreasonable results At the end of a race, a runner accelerates opposite to the motion from a velocity of 9.00 m/s at a rate of 2.00 m/s². (a) How far does she travel in the next 5.00 s? (b) What is her final velocity? (c) Evaluate the result. Does it make sense?

a) (a) -10 m, (b) -1 m/s, (c) No
b) (a) 10 m, (b) -1 m/s, (c) Yes
c) (a) 20 m, (b) 1 m/s, (c) No
d) (a) 20 m, (b) -1 m/s, (c) Yes

Answer 1

The runner will travel a certain distance and end up with a final velocity that doesn't make sense.

Step-by-step explanation:

In this case, the runner starts with a velocity of 9.00 m/s and decelerates at a rate of 2.00 m/s². To find the distance traveled in the next 5.00 seconds, we can use the equation:

d = v0t + 0.5at²

where

d is the distance traveled

v0 is the initial velocity

t is the time

a is the acceleration

Plugging in the given values:

d = (9.00 m/s)(5.00 s) + 0.5(-2.00 m/s²)(5.00 s)²

Simplifying this equation will give you the distance traveled.

For the final velocity, we can use the equation:

v = v0 + at

where

v is the final velocity

Plugging in the given values:

v = 9.00 m/s + (-2.00 m/s²)(5.00 s)

Simplifying this equation will give you the final velocity.

To evaluate the result, we can compare it to the initial conditions. In this case, the result is a negative final velocity which means the runner is moving in the opposite direction. This does not make sense since the runner should be decelerating in the same direction. Therefore, the result is unreasonable.