Calculating Velocity and Displacement Using Acceleration Formula | Train Example

[MagMag]

I'm a little stuck on this:

Suppose that the acceleration of a train during the interval of time from t=2 s to t=4 s is a=2t m/s^2, and at t=2 s its velocity is 180km/h

Using formulas: Velocity v=ds/dt and acceleration a =dv/dt, determine:

(a) the train’s velocity at t=4 s,

and;

(b) the displacement (change in position) from time t=2 s to t= 4 s



I should really be able to do this but for some reason my mind has frozen so I was hoping for some help or some nudges in the right direction!

Thanks in advance!

 

[Stovebolt]

I'm a little stuck on this:

Suppose that the acceleration of a train during the interval of time from t=2 s to t=4 s is a=2t m/s^2, and at t=2 s its velocity is 180km/h

Using formulas: Velocity v=ds/dt and acceleration a =dv/dt, determine:

(a) the train’s velocity at t=4 s,

and;

(b) the displacement (change in position) from time t=2 s to t= 4 s



I should really be able to do this but for some reason my mind has frozen so I was hoping for some help or some nudges in the right direction!

Thanks in advance!

Given the way the question is asked, you should approach this as a calculus problem rather than a physics problem, so disregard the typical kinematics equations.

You are given a = 2t and a = dv/dt, so it follows that dv/dt = 2t. You are also given the interval of t = 2 to t = 4. Knowing the basics of integral calculus, how do you find the equation for V? (don't forget to add in the initial velocity)

Once you get the equation for V, and given that V = ds/dt, how do you find an equation for distance travelled?