Question

the position of an object moving along y axis is given by y=5t^2 where t is measured in seconds what it is velocity at t=3sec and t=5sec and also find out the average velocity of the object between t=3sec and t=5sec ​

Answer 1

GiveN :

• y = 5t² m

To FinD :

• Velocity at t = 3s
• Velocity at t = 5s
• Average velocity between 3 and 5s

SolutioN :

$\implies \sf{y\ =\ 5t^2} \\ \\ \\ \implies \sf{\dfrac{dy}{dt}\ =\ 5(2)t} \\ \\ \\ \implies \sf{v\ =\ ( 10t)\ ms^{-1}}$

_____________________

Put t = 3s

⇒v1 = 10(3)

⇒v1 = 30 m/s

____________________

Put t = 5s

⇒v2 = 10(5)

⇒v2 = 50 m/s

___________________

Average Velocity :

⇒V_avg = (v1 + v2)/2

⇒V_avg = (30 + 50)/2

⇒V_avg = 80/2

⇒V_avg = 40 m/s

➜ Average velocity is 40 m/s