The distance covered by a car at a time, t is given by X=20t+6t^4, calculate (i) the instantaneous velocity when t=1 (i) the instantaneous acceleration when t=1

(i) Instantaneous velocity at t = 1 will be : -

v (t=1) = 44 m/s

(ii) Instantaneous acceleration at t = 1 will be : -

a (t=1) = 72 m/s²

Explanation:

(i) Instantaneous velocity is defined as the time - derivative of displacement, i. e,

v =.

or, v =

or, v = 20 + 24t³

Hence, instantaneous velocity at t = 1 will be

v (t=1) = 20 + 24 (1) ³

or, v (t=1) = 20 + 24

or, v (t=1) = 44 m/s

(ii) Instantaneous acceleration is defined as the time - derivative of velocity, i. e,

a =.

or, v =

or, v = 72t²

Hence, instantaneous acceleration at t = 1 will be

a (t=1) = 72 (1) ²

or, a (t=1) = 72 m/s².