Question

The displacement of a particle moving in one dimension under the action of a constant force is related to the time t by the equation t = square root of x + 3, where x is in metre and t is in seconds. find velocity and acceleration at t=2.​

Answer 1

Given :-

Displacement of particle = x(t) = t = √x+3

x = t² - 3

Here, we will differentiate X(t) w.r.t 't' in order to get Velocity of Particle and after getting Velocity we will again differentiate Velocity w.r.t 't' in order to get acceleration of particle at t = 2s.

v = dx/dt

v = d(t² - 3)/dt

v = 2t

Again, Differentiating,

a = dv/dt

a = d(2t)/dt

a = 2 ms-²

Hence,

Acceleration of the body is independent of time = a = 2 ms-².

Here, velocity comes in terms of 't' but we are asked to find acceleration at t = 2s, so we cannot put t = 2s in Velocity.