Question

Equation of position x with time (t) is given by equation x = 3t³ + 7t² + 5t + 8. The acceleration at time t = 1 sec is

(1) 18 m/sec². 

(2) 32 m/sec². 

(3) Zero 

(4) 14 m/sec². 

Answer 1

Answer is (2) 32 m/sec².

x = 3t³ + 7t² + 5t + 8.

dx/dt = velocity = 3(3t²) + 7(2t) + 5.

= 9t² + 14t + 5.

d²x/dt² = acceleration = 9(2t) + 14 = 18t + 14.

at t =1, d²x/dt² = (18t + 14)_t=1 = 18 + 14 = 32m/s².