Question

Diego runs a 100-meter race. 6 seconds after the race started Diego is 40 meters from the starting line and reaches his max speed; he runs at this max speed for the rest of the race. Diego notices that he is 76 meters from the starting line 10 seconds after the race started.

a. What is Diego's max speed?
b. Suppose Diego runs for an additional 3 seconds after reaching his max speed...
-How far will Diego travel during those additional 3 seconds?
-What is Diego's distance from the starting line 9 seconds after the race started?
c. What is Diego's distance from the starting line 7.5 seconds after the race started?

Answer 1

a. 9m/s b. 27m, 67m c. 53.5m

Explanation:

we have 6 seconds of acceleration linear motion and 4 seconds of constant velocity linear motion.

after the first 6 seconds he is 40 meters from the starting line, the he reaches his max speed and after 4 seconds he is 76-40=36 meters from the point he started running max speed

then, max speed

`v=(x)/(t) =(36m)/(4sec) =9m/s`

v=9m/s

if he runs for an additional 3 seconds after reaching his max speed

`x=v.t=9m/s . 3sec=27m`

x=27m

then, distance from the starting line 9 seconds after the race started

`X=40m+x=40m+27m=67m`

X=67m

if he runs for an additional 1.5 seconds after reaching his max speed (7.5 from the starting line)

`x=v.t=9m/s . 1.5sec=27m`

x=13.5m

then, distance from the starting line 9 seconds after the race started

`X=40m+x=40m+13.5m=53.5m`

X=53.5m