AS integrationWatch

#1
Question:

A particle starts from rest and moves in a straight line. Its speed for the first 3 s is proportional to , where t is the time in seconds from the commencement of motion, and thereafter it travels with uniform speed at the rate it had acquired at the end of the 3rd second. Prove that the distance travelled in the first 3 s is two-thirds of the distance travelled in the next 3 s.

I understand the first 3 seconds is proportional to speed thus
t = 3
thus speed
from here i am stuck I dont know what to do
Last edited by bigmansouf; 1 week ago
0
1 week ago
#2
(Original post by bigmansouf)
Question:

A particle starts from rest and moves in a straight line. Its speed for the first 3 s is proportional to , where t is the time in seconds from the commencement of motion, and thereafter it travels with uniform speed at the rate it had acquired at the end of the 3rd second. Prove that the distance travelled in the first 3 s is two-thirds of the distance travelled in the next 3 s.

I understand the first 3 seconds is proportional to speed thus
t = 3
thus speed
from here i am stuck I dont know what to do
Split it into two parts, up to 3 seconds and then after 3 seconds.
The distance is is the integral of velocity and for the second 3 seconds, the velocity is constant and is equal to the velocity with t=3.
Try setting up those terms and posting if you have problems?
1
1 week ago
#3
Intuitively, it's too easy...

You are comparing the following
0
#4
(Original post by casperyc)
Intuitively, it's too easy...

You are comparing the following
thank you
0
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