Question

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

Answer 1

Answer:

(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.

Explanation: