Question

I slow down to see if they are still behind me. There they are. I accelerate at 4.5 m/s/s. Up ahead is a 75 meter long tunnel. I pass through the tunnel in 2.8 seconds. How long will it take me to reach a speed of 80 m/s

Answer 1

It will take approximately 14.2 seconds to reach a speed of 80 m/s.

Step-by-step explanation:

To determine the time required to reach a speed of 80 m/s, we can use the kinematic equation:

`\[v_f = v_i + a \cdot t.\]`

Where:

`- \(v_f\)` is the final velocity (80 m/s),

`- \(v_i\)` is the initial velocity (0 m/s, as the speed is initially not given),

`- \(a\)` is the acceleration (4.5 m/s²), and

`- \(t\)` is the time.

Rearranging the equation to solve for time
`(\(t\))`, we get:

`\[t = (v_f - v_i)/(a).\]`

Since the initial velocity
`(\(v_i\))` is not provided, we assume it to be 0 m/s.

`\[t = \frac{80 \, \text{m/s} - 0 \, \text{m/s}}{4.5 \, \text{m/s²}}.\]`

Solving the expression gives us the time
`(\(t\))` it takes to reach a speed of 80 m/s. Substituting the values:

`\[t \approx (80)/(4.5) \approx 17.78 \, \text{seconds}.\]`

However, the question mentions passing through a 75-meter tunnel in 2.8 seconds, so we subtract this time:

`\[t_{\text{adjusted}} = 17.78 - 2.8 \approx 14.2 \, \text{seconds}.\]`

Therefore, it will take approximately 14.2 seconds to reach a speed of 80 m/s.