# Speed-Time Graph

• September 14th 2011, 02:38 AM
Ilsa
Speed-Time Graph
A cyclist starting from rest accelerates uniformly to his maximum speed of 12m/s, which he then maintains for the next 3.6 km. He then applies his brakes and decelerates to rest at a rate numerically equal to three times his acceleration. Sketch a speed-time graph and find the total time the cyclist is in motion if the total distnace moved is 3744 m.
• September 14th 2011, 01:52 PM
skeeter
Re: Speed-Time Graph
Quote:

Originally Posted by Ilsa
A cyclist starting from rest accelerates uniformly to his maximum speed of 12m/s, which he then maintains for the next 3.6 km. He then applies his brakes and decelerates to rest at a rate numerically equal to three times his acceleration. Sketch a speed-time graph and find the total time the cyclist is in motion if the total distnace moved is 3744 m.

make a sketch?

for the first " $t$ " seconds ...

$v_0 = 0$ , $v_f = 12$ , let acceleration = $a$

during the constant speed, you know speed and distance ... calculate the time.

for the last " $t/3$ " seconds (why $t/3$ ???) ... acceleration = $3a$ , $v_0 = 12$ , $v_f = 0$

finally, distance speeding up + distance slowing down = 144 m

solve for t and sum up all the times.

I get total time = 324 sec