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
Create a free account to view solution
View Solution FreeMore Kinematics Questions
At what temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47o C?...A particle is moving in x - y plane at 2 m/s along x - axis. 2 seconds later, its velocity is 4 m/s in a direction makin...A disc which several groves are cut along the chord drawn from a ‘A’, is arranged in a vertical plane, survival particle...A particle is projected vertically upwards and it reaches the maximum height H in T seconds. The height of the particle ...The relation time t and distance x is t = αx2 + βx where α and β are constants. The retardation is :...