The derivative dy/dt is not explicitly given. At time t=2, the object is at position (1,8)
a. Find the x-coordinate of the pos. of the object at time t=4.
integral of 3+cos(t^2)dt+1 from 2-4
= 7.133
b. At time t=2, the value of dy/dt is -7. Write an eq for the line tangent to the curve at the point (2,2)
y=8+dy/dx(x-1)
=
y=8+(-7/(3+cos4))(x-1)
c. Find the speed of the object at time=2
speed = square root of (49+(3+cos4)^2)
= 7.383
d. For t greater than or equal to 3, the line tan to the curve at (x,y) has a slope of 2t+1. Find accel. Vector at t=4.
dy/dx=2t+1
d(dy/dt)/dt=-2tsint^2
d(dy/dt)
dt=(2t+1)(3+cost^2)+(-2tsint^2)(2t+1)
=2(3tcos16)+72sin16