Physics teacher has this question for hw.
38. An electric powered model car starts from rest and moves in a straight-line for 4.0 s. The relationship between time and position is x^2+ 2 t^2 = 32, t in seconds and x in cm. Find the velocity at t= 1 s & t = 3 s.
he gave us the answer 0.4 cm/s and 1.5 cm/s for 1 and 3 respectively. I have no clue how to get there (regarding this question there is usually only 1 variable)
well, if you know elementary calculus, it is a trivial question:
x^2+ 2 t^2 = 32 taking derivatives
2x *v+4t=0
v=-2t/x
so, first find the position at t=1
x^2=32-2
x= +-sqrt30 one solution
v= -2*1/sqrt30=-.4
second solution: x=-sqrt30
v= 2/sqrt30= .37cm or .4cm
then do the same for the second time.
Now notice there are two solutions to the quadratic. The teacher should have told you the DIRECTION (ie velocity sign) the movement was in. Moving in a straight line is not descriptive enough for a definite answer.
Now, Non calculus. You can graph this on a x,t axis, notice it is an elipse. To get the velocity at any t, draw a tangent to the ellipse at the time you are wondering, the slope of the line is velocity at that point.