Question

A cyclist is riding his bike up a mountain trail. When he starts up the trail, he is going 8 m/s. As the trail gets steeper, he slows to 3 m/s in 1 minute. What is the cyclist’s acceleration?

Answer 1

`\boxed {\boxed {\sf a\approx -0.08 \ m/s^2}}`

Step-by-step explanation:

Acceleration can be found by dividing the change in velocity by the time.

`a=(v_f-v_i)/(t)`

The final velocity is 3 meters per second. The initial velocity is 8 meters per second.

We need to convert the time to seconds.

• t= 1 minute
• 60 seconds = 1 minute
• t=60 seconds

So, we know that:

`v_f=3 \ m/s \\v_i= 8 \ m/s\\t= 60 \ s`

Substitute the values into the formula.

`a=(3 \ m/s - 8 \ m/s)/(60 \ s)`

Solve the numerator.

• 3 m/s - 8 m/s = -5 m/s

`a=(-5 \ m/s)/(60 \ s)`

Divide.

`a=-0.0833333333 \ m/s/s`

Let's round to the nearest hundredth.

The 3 in the thousandth place tells us to leave the 8 in the hundredth place.

`a\approx -0.08 \ m/s^2`

The cyclist's acceleration is about
`\boxed {-0.08 m/s^2}`