Question

boy as a velocity varying with time given as v is equal to 2t^2/3 then the acceleration of the boy at the given time t=4s is​

Answer 1

V = 2t^2/3 = 2/3 x t^2

Dv/dt = 2/3 x 2 x t
A = 2/3 x 2 x 4
A = 16/3 m/s^2

Answer 2

Answer: a=16/3 m*m/s

Explanation: Given: $v=2t^2/3$.......(1)

To find: acceleration=? at t=4s

Solution: Let acceleration of the boy with which he is moving be "a"

Therefore, we have to find a

We know that $a=dv/dt$

(∵ acceleration is also defined as the differentiation of velocity with respect to time)

Differentiating both sides with respect to time in (1)

We get,

$dv=d(2t^2/3)/dt$

∴$a=4t/3$                      (∵ Differentiation of $t^2=2t$ and $dv/dt=a$)

Now the value of t as t=4s where s is seconds

We get,

∴$a=4(4)/3\\a=16/3 m^{2}/s$ where m is in meters and s is in seconds

hence the required answer to the question is a=16/3 m*m/s

#SPJ2