Question

Distance of particle along a straight line x=50t²+180t find (1) intial velocity (2) velocity at 4sec (3) acceleration of particle

Answer 1

x = 50t²+180t

1) Initial velocity, that is t= 0

Now,

v =dx/dt = d50t²+180t/dt = 100t+180

Initial Velocity = 100×0 +180 = 180m/s

2) Velocity at t= 4

v = 100t+180 = 100×4+180 = 580m/s

3) Acceleration

a = dv/dt = d100t+180/dt = 100m/s²

We know, the differentiation of displacement gives instantaneous velocity and differentiation of velocity gives instantaneous accelration.

Cheers!