Question

The velocity of a particle moving along x-axis is given by v(t) = 4 alpha middot t^2 - beta middot t in m/s. (a) Find the units of measurement of the known constants alpha and beta. (b) Find the average acceleration of the particle during its first 5 s of its motion. (c) When does the particle stop momentarily? (d) How far is the particle from the origin at that instant, if x(t = 0) = 0? (e) Find the instantaneous acceleration at t = 0 s. [Your answers should be given in terms of alpha and beta]

Answer 1

V(t) = 4 alpha t^2 - beta t same dimensions can be add or subtract. alpha = m/s/s^2 = m/s^2 beta = m/s/s = m/s^2 avg accl^n = Delta v vector/Delta t = v(t = 5) - v(t = 0) /5 = (100 alpha - 5 beta) - (0) /5 = 20 alpha - beta momentarily steps at t = ? v = 0 4 alpha t^2 - beta t = 0 t = beta/4 alpha. Now v = 4 alpha t^2 - beta t = dx/dt integral [dx]^x_0 = integral [4 alpha t^2 - beta t]^t = beta/4 alpha_0 x = [4 alpha t^3/3 - beta t^2/2]^beta/4 alpha_0 x = beta^3/48 alpha^2 - beta^3/32 alpha^2 = -beta^3/96 alpha^2 G inst = dv/dt = 8 alpha t - beta = -beta (at t = 0)