how to find the distance given the velocity?

[gen_shao]

starting at rest . the velocity of an object is given by v = 3t^2 . Find the distance traveled after 5 seconds.my solution:d =vtbut v = 3t^2so: d = (3t^2)(t)@t=5d = [3(5)^2](5)d = [3(25)](5)d = 75(5)d = 375 unitsmy answer is obviously correctbut the answer in the book is d=125.please tell me if the book is wrong or i am wrong,if i am wrong, please explain why i am wrong.. ty..

 

[Deleted member 4993]

starting at rest . the velocity of an object is given by v = 3t^2 . Find the distance traveled after 5 seconds.my solution:d =vtbut v = 3t^2so: d = (3t^2)(t)@t=5d = [3(5)^2](5)d = [3(25)](5)d = 75(5)d = 375 unitsmy answer is obviously correctbut the answer in the book is d=125.please tell me if the book is wrong or i am wrong,if i am wrong, please explain why i am wrong.. ty..

Incorrect .... d = vt is true for constant 'v'.

When v is a function of t, you neeed to start with:

v = ds/dt

so

ds/dt = 3t^2

Now integrate and calculate the distance.