Question

The velocity of a particle moving in a straight line varies with time as v = A + Bt, where t is time. The acceleration of particle is

AB

B/A

B

A​

Answer 1

Given : The velocity of a particle moving in a straight line varies with time as v = A + Bt, where t is time.

To Find : The acceleration of particle

AB

B/A

B

A​

Solution:

acceleration is rate of change of velocity

v =  A + Bt

dv/dt  =  B

acceleration  = dv/dt

Hence acceleration  = B

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Answer 2

Given:

The velocity of a particle moving in a straight line varies with time as v = A + Bt, where t is time.

To find:

Acceleration of particle?

Calculation:

$\rm \: v = A + Bt$

Now, acceleration can be found out by differentiation of velocity function with respect to time :

$\rm \implies \: a = \dfrac{dv}{dt}$

$\rm \implies\: a = \dfrac{d(A + Bt)}{dt}$

$\rm \implies\: a = \dfrac{dA}{dt} + \dfrac{d(Bt)}{dt}$

$\rm \implies\: a = B \: units$

So, acceleration of object is B units.