physics, simple equations. Help

Question

Task 1.

Velocity to a particle is shown quadratic with the time (t)

v(t)=1/2 Bt^2 (B is for beta)

a) What is the acceleration, and the Equation for the distance made by time?

b) Lets say B = 2 m/s^3. how big is the acceleration at t1 = 1 s, and t2= 3s. How big is the smaller acceleration in the time interval between t2 - t1?

Answer 1

(a) V=1/2Bt^2. acceleration= a = dv/dt=Bt. distance (x) = integral (v)= 1/6Bt²+X₀ ( constant of the integration as well as the initial position)

(b)plugging the numbers ====> t=1s ===> a= Bt= 2 m/s², and at t=3s ========> a=6m/s², since the relation between a and t is linear the maximum would be at t=3s