Hello
Problem statement:
Cars A and B are going in the same direction and are are next to each other at t=0 at which point car A has a velocity of 0 and car B has a velocity of 10. Car a has an acceleration of 2 and car B has an acceleration of 0,6t. Calculate at what value of t(time) will they be next to each other again.
Solution so far:
Step 1.
Car A a(t)=2 --> v(t)=2t+c --> c=v0 and v0 = 0 because v@ t=0 is 0
Car B a(t)=0,6t --> v(t)=0.3t2+c --> c=v0 and v0 is 10 because v@t0=10
Step 2.
Car A s(t)=t2+c --> c=s0 and s0=0 and thats an assumption on my part
Car B s(t)= 0,1t3+10t+c and c is also 0 for the reason above
Step 3.
In order to figure out the time at which these 2 cars meet again i just made s(t)a=s(t)b, so
t^2=0,1t3+10t --> 0,1t3-t2+10t=0
and the solutions would follow: t=0, t=5+5\sqrt{3}i, t=5-5\sqrt{3}i, or t=0, t= 13.66, t=-13.66 and i would pick the 13.66 positive answer
Am i missing anything? is it correct?
Thanks in advance
Problem statement:
Cars A and B are going in the same direction and are are next to each other at t=0 at which point car A has a velocity of 0 and car B has a velocity of 10. Car a has an acceleration of 2 and car B has an acceleration of 0,6t. Calculate at what value of t(time) will they be next to each other again.
Solution so far:
Step 1.
Car A a(t)=2 --> v(t)=2t+c --> c=v0 and v0 = 0 because v@ t=0 is 0
Car B a(t)=0,6t --> v(t)=0.3t2+c --> c=v0 and v0 is 10 because v@t0=10
Step 2.
Car A s(t)=t2+c --> c=s0 and s0=0 and thats an assumption on my part
Car B s(t)= 0,1t3+10t+c and c is also 0 for the reason above
Step 3.
In order to figure out the time at which these 2 cars meet again i just made s(t)a=s(t)b, so
t^2=0,1t3+10t --> 0,1t3-t2+10t=0
and the solutions would follow: t=0, t=5+5\sqrt{3}i, t=5-5\sqrt{3}i, or t=0, t= 13.66, t=-13.66 and i would pick the 13.66 positive answer
Am i missing anything? is it correct?
Thanks in advance