I was doing my maths hw when i got stuck on this M1 exam paper question.
3. In a simple model for the motion of a car, its velocity,v, at time t seconds is given by
v=(3t² - 2t + 8)i + (5t +6)j ms-¹
a) Calculate the speed of the car when t=0.
b) Find the values of t for which the velocity of the car is parallel to the vector (i+j).
c) Why would this model not be appropriate for large values of t?
I have done a) and made it 10ms-¹ which agrees with the answers i have been supplied. I am confused on how to do b) and any help would be appreaciated.
if a vector ai+bj is parallel to the vector i+j, it means ai+bj=k(i+j)
since i and j are not parallel to each other, the only solution is a=k, b=k
for your question
3t² - 2t + 8=5t +6
t=1/3 or t=2
for c, the speed cannot grow up forever.
Oh, and "c" is because of "c"