Question

The position x (in metre) of a particle along a straight
line is given as x = 3t
2 – 18t. The maximum speed
in the time interval t = 0 to t = 2 s is
(1) 18 m/s (2) 6 m/s
(3) 12 m/s (4) 20 m/s

Answer 1

Explanation:

diffrentiate the equation with respect to dt

dx/dt=6t-18

v=6t-18

put t=0

v=-18

put t=2

v=12-18

v=-6

so option1 is correct

Answer 2

Given:

Equation for position of x = (3t^2-18t)

To find:

Maximum speed of the particle in the time interval t=0 to t=2.

Solution:

We will differentiate the equation for the position of the particle to get the equation of velocity:

dx/dt = 6t - 18

v = 6t - 18

T get the value of v at t = 0

v = -18

At t= 2, v= -6

So, the speed at t=2 will be 6m/s in the opposite direction.

The correct option is 2 i.e. 6m/s.