Question

on a
16. The position of a particle moving straight line
path is given by X= 12+18t +9t2 metees

What is the instantaneous acelacation?
a=d2x/dt2

Answer 1

Answer:

18 m/s²

Explanation:

instantaneous velocity dv = ds/dt

=> dv = d(12 + 18t + 9t²)/dt

= 0 + 18(1) + 2(9)t

= 18 + 18t

instantaneous acceleration da = dv/dt

=> da = d(18 + 18t)/dt

= 0 + 18(1)

= 18

Instantaneous acceleration is 18 m/s².

d²x/dt² refers to double differentiation which mean differentiating twice which we have done (differentiating dx, then dv)

Answer 2

Given:-

• A particle moving straight line
• path is X= 12+18t +9t2 meters.

To find:-

• Instantaneous acelacation

Solution:-

Velocity = dx/dt = 18 + 18t

⟹ da = d(18 + 18)/dt

⟹ 0 + 18(1)

⟹ = 18