Question

Corey runs a 100-meter race. 7 seconds after the race started Corey is 45 meters from the starting line and reaches his max speed; he runs at this max speed for the rest of the race. Corey notices that he is 80 meters from the starting line 12 seconds after the race started. What is Corey's max speed? meters per second Suppose Corey runs for an additional z seconds after reaching his max speed... How far will Corey travel during those additional z seconds? meters What is Corey's distance from the starting line 7 + z seconds after the race started? meters What is Corey's distance from the starting line x seconds after the race started (provided x ≥ 7 )?

Answer 1

Answer:

• Corey's max speed is $7 \frac{m}{s}$
• the distance Corey's covers in z seconds is $7 \frac{m}{s} * z \ s$
• $d (z) = 45 m + 7 \frac{m}{s} * z$
• $d (x) = 45 m + 7 \frac{m}{s} * (x-7 s)$

Explanation:

Corey's max speed

For constant speed, we know:

$v=\frac{distance}{time}$

The distance between the 80 meters and the 45 meters is:

$distance = 80 m - 45 m = 35 m$

and the time it took to reach the 80 meter will be:

$time = 12 s - 7 s = 5 s$

So, Corey's max speed is

$v_{max}=\frac{35 m}{5 s} = 7 \frac{m}{s}$

How far runs Corey

As the velocity of Corey's is $v_{max}$, the distance Corey's covers in z seconds is

$distance = v_{max} * z \ s$

$distance = 7 \frac{m}{s} * z \ s$

What is Corey's distance from the starting line

At time 7 + z seconds the distance will be the 45 meters he covers in the first part of the race plus the distance he traveled at constant speed. this is:

$d (z) = 45 m + v_{max} * z$

$d (z) = 45 m +7 \frac{m}{s} * z$

At time x ( x greater or equal to 7 seconds) the distance will be the 45 meters he covers in the first part of the race plus the distance he traveled at constant speed. this is:

$d (x) = 45 m + v_{max} * (x-7 s)$

$d (x) = 45 m + 7 \frac{m}{s} * (x-7 s)$