Not sure if I understood the questions correctly.
First question
At 5s, speed = 3.2*5 = 16m/s
And centripetal acceleration at 16m/s = v^2/r = 14.222222 m/s^2
To find magnitude of acceleration when t=5, use pygathoras
theroem.
magnitude = sqrt(14.222222^2 + 3.2^2) = 14.58 m/s^2
2nd question
When x=3, y = sqrt(4*3^3 +8*3) = 11.489
differentiate w.r.t. time
2y dy/dt = 12x^2 dx/dt + 8
When x=3, dx/dt=7, y=11.489 => dy/dt = 33.249
differentiate w.r.t. time
2y d2y/dt2 + 2 (dy/dt)^2 = 12x^2 d2x/dt2 + 24x (dx/dt)^2
when x=3, dx/dt=7, d2x/dt2=7, y=11.489, dy/dt = 33.249
d2y/dt2 = 90.217
Hence, magnitude of normal component of acceleration =
sqrt(90.217^2 + 7^2) = 90.5 m/s^2
Not sure if this is what you want.
Regards,
Eagle
Owner of Strategic Tuition
