Question

The motion of a particle is defined by the relation x = t4 - 10t2 + 8t + 12, where x and t are expressed in inches and seconds, respectively. Determine the position, the velocity, and the acceleration of the particle when t = 1s.​

Answer 1

Answer:

2 inch/sec

- 8 inch/sec²

Explanation:

velocity = dx/dt

velocity = d(t^4 - 10t^2 + 8t + 12)/dt

velocity = 4t³ - 20t + 18

At = 1, velocity = 4(1)³ - 20(1) + 18 = 2

Velocity at t = 1 is 2 inch/sec

Acceleration = dv/dt

Acceleration = d(4t³ - 20t + 18)/dt

Acceleration = 12t² - 20

At t = 1, acceleration = 12(1)² - 20 = -8

Acceleration at t=1 is - 8inch/sec²

Answer 2

Answer:

Given:

at t=1 sec

x=11 m

dx/dt=4t^3+20t+8=v

at t=1 sec

v=32 m/s

a=12t^2+20

at t= 1 sec

a=32 m/s^2