Question

the position of a body is given by x=at+4bt^3 where a and b are constants x is position and t is time. find velocity and acceleration at t=5seconds

Answer 1

a=dv/dt

v=ds/dt

here s=At+4Bt^3

v=A+12Bt^2

a=24Bt.→this is the acceleration

Answer 2

Answer:

Velocity, v = a + 300 b

Acceleration, a = 120 b

Explanation:

It is given that, the position of a body is given by :

$x=at+4bt^3$

Where

a and b are constants and t is time

Velocity is given by : $v=\dfrac{dx}{dt}$

$v=\dfrac{d(at+4bt^3)}{dt}$

$v=a+12bt^2$

At t = 5 seconds, v = a + 300 b

Acceleration is given by : $a=\dfrac{dv}{dt}$

$a=\dfrac{d(a+12bt^2)}{dt}$

a = 24 bt

At t = 5 seconds, acceleration, a = 120b

Hence, this is the required solution.