Question : The motion of a particle along a straight line is described by the function x=(2t-3)², where x is in metre and 't' in seconds. The velocity of the particle at t=2 sec is ________. (in m/s)
Doubt by Suhani
Solution :
Here
x=(2t-3)²
differentiating both sides w.r.t time t
dx/dt = d(2t-3)/dt
v= 2(2t-3) d(2t-3)/dt
v= 2(2t-3)(2-0)
v= 2(2t-3) d(2t-3)/dt
v= 2(2t-3)(2-0)
v=4(2t-3)
velocity at t=2sec
v | t=2 = 4[2(2)-3]
v | t=2 = 4[4-3]
v | t=2 = 4[1]
v | t=2 = 4 m/s
v | t=2 = 4[2(2)-3]
v | t=2 = 4[4-3]
v | t=2 = 4[1]
v | t=2 = 4 m/s
Hence, the required velocity at t = 2 sec is 4 m/s.
Similar Question :
The motion of a particle along a straight line described by the function x=(2t-3)², where x is in metre and time t is in second. Then, the velocity of the particle at origin is
a) 0
b) 1
c) 2
d) 4