KinematicsHard
Question
The position (x) of a particle at any time (t) is given by
x(t) = 4t3 - 3t2 + 2
The acceleration and velocity of the particle at any time t = 2 sec are respectively
x(t) = 4t3 - 3t2 + 2
The acceleration and velocity of the particle at any time t = 2 sec are respectively
Options
A.16 ms-2 and 22 ms-1
B.42 ms-2 and 36 ms-1
C.48 ms-2 and 36 ms-1
D.12 ms-2 and 25 ms-1
Solution
we have x(t) = 4t3 - 3t2 + 2
⇒ v =
= 12t2 - 6t
and a = = 24t
∴ v at t = 2s is 12 (2)2 - 6(2)i.e., 36 ms-1
and a at t = 2s is 24 × 2i.e., 48 ms-2
⇒ v =
= 12t2 - 6tand a =
= 24t ∴ v at t = 2s is 12 (2)2 - 6(2)i.e., 36 ms-1
and a at t = 2s is 24 × 2i.e., 48 ms-2
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