Question

The position of an object is given by x=At+Bt2, where x is in meters and t is in seconds. What is the acceleration at 2 s

Answer 1

x=At+Bt^2

V=dx/dt=A+2Bt

acceleration a=d^2x/dt^2=2B

Hence 2B is the acceleration at any time coz t is not there in acceleration.

So, acceleration will not depend on time.

Answer 2

Given :

An equation x =At + Bt²

To Find :

Acceleration at t = 2 sec

Solution :

Given, x = At + Bt²

∴ Velocity of the object (v) = $\frac{dx}{dt}$

                                            = $\frac{d}{dt} (At + Bt^2)$

                                            = (A + 2Bt) m/sec

∴ Acceleration of the object (a) = Rate of change of velocity

                                                    =  $\frac{dv}{dt}$

                                                    = $\frac{d}{dt} (A + 2 Bt)$

                                                    = 2B m/sec²

As acceleration is independent of time 't'.

∴ The acceleration of the object at 2 sec is 2B m/sec²